Question 1

Write an equation to represent the problem.
-Michele has a dollhouse, (which is an exact replica of her "real" house), in which the size of the dollhouse is 1 th the size of her "real" house. The difference between the length of a side of her "real" house and the length
16
Of a side of her dollhouse is 96 feet.
A) 
B)  = 0
C)  = 96
D)  = 96

Accepted Answer

Let x be the length of a side of the "real" house. Then the length of a side of the dollhouse is x/10 (since it is 1/10 the size of the "real" house). We are told that the difference between the lengths of a side is 96 feet, so we can set up the equation x - x/10 = 96 and simplify to get 9x/10 = 96. Solving for x, we get x = 960/9 = 106.67 feet. Therefore, the length of a side of the dollhouse is x/10 = 10.67 feet, which is indeed 96 feet less than the length of a side of the "real" house. Thus, C is the correct choice. Let x be the length of a side of her "real" house. Then, the length of a side of her dollhouse is x/10 (since the size of the dollhouse is 1/10 the size of her "real" house). The difference between the length of a side of her "real" house and the length of a side of her dollhouse is given as 96 feet. So the equation is:

x - x/10 = 96

Simplifying this equation, we get:

9x/10 = 96

Multiplying by 10/9 on both sides, we get:

x = 960/9

Therefore, x = 106.67 (rounded to two decimal places). This means that the length of a side of her "real" house is approximately 106.67 feet.

The difference between the length of a side of her "real" house (106.67 feet) and the length of a side of her dollhouse (106.67/10 = 10.67 feet) is indeed 96 feet, which is given in the problem. Therefore, the best choice is C.

Question 2

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-The sum of a number and 2 is 7.
A) x - 2 = 7; 9
B) x + 2 = 7; 5
C) x ÷ 2 = 7; 14
D)

Accepted Answer

The equation that can be set up is x + 2 = 7.
Solving the equation, we get x = 5.
Therefore, the correct choice is B. Let x be the number.
The equation that represents the problem is:
x + 2 = 7
Solving for x:
x = 7 - 2
x = 5
Therefore, the number is 5, and the best choice is B.

Question 3

Write an equation to represent the problem.
-The difference of twice a number and 10 is 14.
A) 2x + 10 = 14
B) x - 2 ·10 = 14
C) 10 - 2x = 14
D) 2x - 10 = 14

Accepted Answer

"Twice a number" can be represented as 2x, and "the difference of...and 10" means to subtract 10 from the expression. Therefore, we get the equation 2x - 10 = 14. "Twice a number" can be represented as 2x. 
So, "the difference of twice a number and 10" is 2x - 10. 
And the problem states that this is equal to 14. 
Therefore, the equation becomes 2x - 10 = 14.

Question 4

Write an equation to represent the problem.
-Markus Lawson is 4 years older than three times Pam Lincoln's age. The sum of their ages is 73. Let a represent Pam's age.
A) a + (3a - 4) = 73
B) a + (3a + 4) = 73
C) a - (3a + 4) = 73
D) a + (a + 34) = 73

Accepted Answer

The correct equation is a + (3a + 4) = 73 because Markus is 4 years older than three times Pam's age, so Markus' age is represented by 3a + 4. The sum of their ages equals 73, leading to the equation a + (3a + 4) = 73.

Question 5

Write an equation to represent the problem.
-Jennifer Park's 2007 income was 6.9% greater than her 2006 income. Her income in 2007 was $78,100. Let i represent 2006 income.
A) i - 0.069i = 78,100
B) 2i + 0.069i = 78,100
C) i + 0.069·78,100 = 78,100
D) i + 0.069i = 78,100

Accepted Answer

If Jennifer's 2006 income is represented by i, then her 2007 income is i + 0.069i, which simplifies to 1.069i. We are given that 1.069i = $78,100, so we can write the equation i + 0.069i = $78,100, which is equivalent to choice D. If Jennifer Park's 2007 income was 6.9% greater than her 2006 income, we can represent it as the equation:
2007 income = 2006 income + 0.069(2006 income)
or
2007 income = 1.069(2006 income)
We are given that her 2007 income was $78,100:
2007 income = $78,100
Substituting this value in the equation, we get:
1.069(2006 income) = $78,100
Simplifying the equation:
2006 income = $73,400
Therefore, the equation that represents the problem is:
i + 0.069i = 78,100
which simplifies to:
1.069i = 78,100
and the value of i is $73,400.

Question 6

Write the indicated expression.
-Kevin and Amir share in the profits of a pet supplies store. If the total profit is $80,000 and p is the amount of profit Keven receives, write an expression for the amount Amir receives.
A) p - $80,000
B) p + $80,000
C) $80,000 - p
D) $80,000 + p

Accepted Answer

Since the total profit is $80,000 and Kevin receives an amount p, that means Amir must receive the remaining profit, which is $80,000 - p. Therefore, the expression for the amount Amir receives is $80,000 - p. Since Kevin and Amir share the total profit of $80,000, the expression for the amount Amir receives can be written as "total profit - Kevin's profit" or "$80,000 - p". Therefore, the correct answer is C.

Question 7

Write the indicated expression.
-The smaller of two numbers is 52 less than four times the larger number. Write an expression for the smaller number subtracted from the larger number. Let n represent the larger number.
A) 4n - (n - 52)
B) n - (n - 4·52)
C) n - (4n - 4·52)
D) n - (4n - 52)

Accepted Answer

We know that the smaller number is 52 less than four times the larger number, so we can write an equation: smaller number = 4n - 52. To find the difference between the two numbers (which is what the expression is asking for), we take the larger number minus the smaller number: n - (4n - 52). Simplifying this expression gives us D: n - 4n + 52 = -3n + 52. The smaller number can be represented as 4n - 52 (since it is 52 less than four times the larger number).
Therefore, the expression for the larger number minus the smaller number would be:
n - (4n - 52) which simplifies to 52 - 3n or equivalently, -3n + 52. This matches the expression in choice D.

Question 8

Write the indicated expression.
-The price of Investor Growth mutual fund is 23% greater than the price of Investor Value mutual fund. Write an expression for the sum of Growth and Values mutual funds. Let n represent the Investor Value.
A) 2n + (n + 0.23n)
B) n + (n + 0.23n)
C) n + 0.23n
D) n + (n - 0.23n)

Accepted Answer

The expression for the sum of the two mutual funds would be n (Investor Value) plus the price of Investor Growth, which is 23% greater than the price of Investor Value, or 0.23n. Therefore, the expression is n + (n + 0.23n), which simplifies to 2n + 0.23n, or option B. Option A adds an extra n that is not necessary, while option C only includes the price of Investor Value and not Investor Growth. Option D subtracts the 23% increase instead of adding it. The expression for the sum of Growth and Value mutual funds should include the price of both funds. Let's call the price of Investor Growth x. We know that x is 23% greater than the price of Investor Value which is represented by n. So we can write x = n + 0.23n or x = 1.23n. The sum of the prices of both funds would be n + x, which can be simplified as n + 1.23n or 2.23n. This matches option B: n + (n + 0.23n), which simplifies to 2n + 0.23n or 2.23n. Therefore, option B is the correct choice.

Question 9

Write an equation to represent the problem.
-Lauren Wolf purchased a dress at a 20% off sale. She paid $114 for the dress. Let p represent the price of the dress.
A) p - 0.2 = 114
B) p - 0.2p = 114
C) 0.2p - p = 114
D) p + 0.2p = 114

Accepted Answer

Since Lauren purchased the dress at a 20% discount, she only paid 80% of the original price. Therefore, the equation representing the problem would be: p - 0.2p = 114. This simplifies to 0.8p = 114, and solving for p, we get p = 142.50, which is the original price of the dress. The equation should represent the original price (p) minus 20% of that price (0.2p) equals the price she paid ($114). So the correct equation is p - 0.2p = 114, which simplifies to 0.8p = 114.

Question 10

Write an equation to represent the problem.
-The sum of a number and 7 is 16.
A) x - 7 = 16
B) 7x = 16
C) x + 7 = 16
D) x ÷ 7 = 16

Accepted Answer

"The sum of a number and 7" can be represented by "x + 7" and "is" usually means equals in math problems. Therefore, the equation would be "x + 7 = 16". The problem states that the sum of a number and 7 is 16, which can be represented by the equation x + 7 = 16. Choice A is incorrect because it subtracts 7 from x instead of adding it. Choice B is incorrect because it multiplies 7 and x instead of adding them. Choice D is incorrect because it divides x by 7 instead of adding 7 to it.

Question 11

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-At the beginning of the year, the odometer on an SUV read 37,532 miles. At the end of the year, it read 52,412 miles. If the car averaged 24 miles per gallon, how many gallons of gasoline did it use during the year?
A) 14,880 gallons
B) 357,120 gallons
C) 620 gallons
D) 62 gallons

Accepted Answer

The SUV traveled 52,412 - 37,532 = 14,880 miles during the year.
To find gallons of gasoline used, divide the distance traveled by the average miles per gallon:

Gallons = Distance / Miles per gallon

Gallons = 14,880 / 24 = 620

Therefore, the SUV used 620 gallons of gasoline during the year. First, we need to find the total number of miles the SUV traveled during the year:

52,412 miles - 37,532 miles = 14,880 miles

Next, we can use the fact that the SUV averaged 24 miles per gallon to find the total gallons of gas used:

Total gallons = Total miles / Miles per gallon

Total gallons = 14,880 miles / 24 miles per gallon

Total gallons ≈ 620 gallons

Therefore, the best choice is C, 620 gallons, as it is the only option that matches our calculated answer.

Question 12

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Andrea decided to rollerblade to her mother's house. Five blocks from her home, one of the wheels on her skate broke, and she had to walk the remaining six blocks to her mother's. She could not repair her skate and had to
Walk all the way back home. How many more blocks did Andrea walk than she skated?
A) 11 blocks
B) 12 blocks
C) 17 blocks
D) 22 blocks

Accepted Answer

The answer of Set up an equation that can be...

Question 13

Write an equation to represent the problem.
-Scot and Elizabeth ate dinner at an upscale bistro. The cost of their meals plus a 16% tip was $63.52.
A) x + 1.6x = 63.52
B) x + 16x = 63.52
C) x + 0.16x = 63.52
D) x + 0.16 = 63.52

Accepted Answer

Let x be the cost of their meals. The tip is 16% of the cost of their meals, which is 0.16x. Therefore, the total cost of their meals plus tip is x + 0.16x = 1.16x. We are told that this total cost is $63.52, so we can write the equation 1.16x = 63.52. Dividing both sides by 1.16 gives x = 54.5, which is the cost of their meals. Therefore, the equation that represents the problem is x + 0.16x = 63.52. Let x be the cost of their meals. The 16% tip is 0.16x. Therefore, the equation should be x + 0.16x = 63.52 since the cost of their meals plus a 16% tip equals $63.52. Option A and B both incorrectly add the percentages to the original cost, while option D doesn't include x in the final equation.

Question 14

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-The difference of twice a number and 10 is 20.
A) x - 2 ·10 = 20; 40
B) 10 - 2x = 20; - 5
C) 2x - 10 = 20; 15
D) 2x + 10 = 20; 5

Accepted Answer

Let the number be x.

"Twice a number" is 2x.

The "difference of twice a number and 10" is 2x - 10.

We know that 2x - 10 is equal to 20, so we can set up the equation:

2x - 10 = 20

Adding 10 to both sides, we get:

2x = 30

Dividing both sides by 2, we get:

x = 15

Therefore, the answer is C, 2x - 10 = 20, and the solution is x = 15. Let x be the number.
According to the problem, the difference of twice a number and 10 is 20 can be written as:
2x - 10 = 20
Solving for x, we can add 10 to both sides:
2x = 30
Dividing both sides by 2, we get:
x = 15
Therefore, the answer is C.

Question 15

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-City A has an elevation of 15,574 feet above sea level while city B has an elevation of 18,476 feet below sea level. How much higher is City A than City B?
A) 2902 ft.
B) 34,150 ft.
C) 34,050 ft.
D) 3002 ft.

Accepted Answer

The total elevation difference between the two cities can be found by adding their elevations.

Total elevation difference = elevation of city A - elevation of city B
Total elevation difference = 15,574 ft - (-18,476 ft) 
Total elevation difference = 15,574 ft + 18,476 ft 
Total elevation difference = 34,050 ft

Therefore, the answer is C) 34,050 ft. To find the difference in elevation between City A and City B, we need to add their elevations.
Total difference = elevation of City A + elevation of City B
Total difference = 15,574 ft + (-18,476 ft) [Note that the elevation of City B is given as a negative value since it is below sea level]
Total difference = -2902 ft
So City A is 2902 feet higher than City B. However, the question asks for the magnitude of this difference (i.e. without a negative sign) which is 2902 feet. Therefore, the answer is C, 34,050 ft is incorrect because it implies that City B is higher than City A.

Question 16

Write an equation to represent the problem.
-Six more than seven times a number is that number increased by 36.
A) 7(x + 6) = x + 36
B) 7x + 6 = 36x
C) 7x - 6 = x + 36
D) 7x + 6 = x + 36

Accepted Answer

To solve the problem, we need to create an equation that represents the given information. Let's call the unknown number "x".

"Six more than seven times a number" can be written as: 7x + 6

"is that number increased by 36" can be written as: x + 36

Putting it all together, we get:

7x + 6 = x + 36

So the answer is D. The equation can be written as 7x + 6 = x + 36, where x is the unknown number. This is because "seven times a number" can be represented as 7x, and "six more than" can be represented as +6. The phrase "that number increased by 36" means the same as "the number plus 36," which is represented as x + 36. The other answer choices do not match the given problem statement.

Question 17

Write an equation to represent the problem.
-Six times a number is 13 more than two times that number.
A) 6 + x = 2x + 13
B) 6x = 2x + 13
C) 6x + 13 = 2x
D) 6x = 2(x + 13)

Accepted Answer

Let the number be x. Then the equation becomes 6x = 2x + 13, since "six times a number" is 6x, and "is 13 more than two times that number" translates to "= 2x + 13." The equation would be 6x = 2x + 13, as "Six times a number" can be represented by 6x, "is" can be represented by an equal sign, and "13 more than two times that number" can be represented by 2x + 13. Option A is incorrect since it adds x to both sides, which is unnecessary. Option C is incorrect since the constant term should be on the opposite side of the equation. Option D is incorrect since it distributes the 2 to x and 13 before combining like terms, which results in the wrong equation.

Question 18

Write the indicated expression.
-The assessed value of Linda Grill's house is 2000 more than twice that of Mel Murphy's house. Write an expression for the sum of the assessed values. Let v represent the value of Mel Murphy's house.
A) v + (2v + 2000)
B) v + (v + 2·2000)
C) v + (v + 2000)
D) v + (2v - 2000)

Accepted Answer

The assessed value of Linda's house is 2v + 2000, where v is the value of Mel's house. The sum of their assessed values is v + (2v + 2000).

Question 19

Write the indicated expression.
-Keerti found that he had y dimes in his pocket. Write an expression that represents this quantity of money in cents.
A) y + 10
B) 
C) 
D) 10y

Accepted Answer

Since there are 10 cents in a dime, the number of cents Keerti has is simply y multiplied by 10, which is represented by 10y. Since each dime is worth 10 cents, the quantity of money in cents is simply 10 times the number of dimes, which is represented by the expression 10y.

Question 20

Write the indicated expression.
-A slice of pie has 200 calories and a scoop of ice cream has 200 calories. If John has x pieces of pie with 3 scoops of ice cream each, write an expression that represents the number of calories he will consume.
A) 3x + 200 + 200
B) 200·3x + 200
C) 200x + 3·200
D) (200 + 3·200)x

Accepted Answer

Each piece of pie has 200 calories, and each scoop of ice cream has 200 calories. If John has x pieces of pie and each piece is accompanied by 3 scoops of ice cream, then the total calories for each piece of pie and its ice cream is 200 (for the pie) + 3*200 (for the ice cream), making the expression for the total calories consumed (200 + 3*200)x.

Quiz 3: Applications of Algebra

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -The sum of a number and 2 is 7.

Write an equation to represent the problem. -The difference of twice a number and 10 is 14.

Write an equation to represent the problem. -Markus Lawson is 4 years older than three times Pam Lincoln's age. The sum of their ages is 73. Let a represent Pam's age.

Write an equation to represent the problem. -Jennifer Park's 2007 income was 6.9% greater than her 2006 income. Her income in 2007 was $78,100. Let i represent 2006 income.

Write the indicated expression. -Kevin and Amir share in the profits of a pet supplies store. If the total profit is $80,000 and p is the amount of profit Keven receives, write an expression for the amount Amir receives.

Write the indicated expression. -The smaller of two numbers is 52 less than four times the larger number. Write an expression for the smaller number subtracted from the larger number. Let n represent the larger number.

Write the indicated expression. -The price of Investor Growth mutual fund is 23% greater than the price of Investor Value mutual fund. Write an expression for the sum of Growth and Values mutual funds. Let n represent the Investor Value.

Write an equation to represent the problem. -Lauren Wolf purchased a dress at a 20% off sale. She paid $114 for the dress. Let p represent the price of the dress.

Write an equation to represent the problem. -The sum of a number and 7 is 16.

Write an equation to represent the problem. -Scot and Elizabeth ate dinner at an upscale bistro. The cost of their meals plus a 16% tip was $63.52.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -The difference of twice a number and 10 is 20.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -City A has an elevation of 15,574 feet above sea level while city B has an elevation of 18,476 feet below sea level. How much higher is City A than City B?

Write an equation to represent the problem. -Six more than seven times a number is that number increased by 36.

Write an equation to represent the problem. -Six times a number is 13 more than two times that number.

Write the indicated expression. -The assessed value of Linda Grill's house is 2000 more than twice that of Mel Murphy's house. Write an expression for the sum of the assessed values. Let v represent the value of Mel Murphy's house.

Write the indicated expression. -Keerti found that he had y dimes in his pocket. Write an expression that represents this quantity of money in cents.

Write the indicated expression. -A slice of pie has 200 calories and a scoop of ice cream has 200 calories. If John has x pieces of pie with 3 scoops of ice cream each, write an expression that represents the number of calories he will consume.