Question 1

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Inclusive of a 7.5% sales tax, a diamond ring sold for $2042.50. Find the price of the ring before the tax was added. (Round to the nearest cent, if necessary.)

Accepted Answer

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Question 2

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-During an intramural basketball game, Team A scored 16 fewer points than Team B. Together, both teams scored a total of 150 points. How many points did Team A score during the game?

Accepted Answer

Let x be the number of points scored by Team B. Then, the number of points scored by Team A is x - 16. Together, both teams scored 150 points, so we can set up the equation: x + (x-16) = 150. Solving for x, we get x = 83. Therefore, Team A scored x-16 = 67 points. Let X be the number of points Team B scored.
Then, Team A scored X - 16 points.
The total number of points both teams scored is 150, so:

X + (X - 16) = 150
2X - 16 = 150
2X = 166
X = 83

Therefore, Team A scored X - 16 = 83 - 16 = 67 points.

The correct answer choice is C, 67 points.

Question 3

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A train ticket in a certain city is $1.50. People who use the train also have the option of purchasing a frequent rider pass for $18.00 each month. With the pass, each ticket costs only $0.75. Determine the number of times in a
Month the train must be used so that the total monthly cost without the pass is the same as the total monthly
Cost with the pass.

Accepted Answer

Let $x$ represent the number of times the train is used in a month. Without the pass, the cost is $1.50x$. With the pass, the cost is $18 + 0.75x$. Setting these equal to find when the costs are the same: $1.50x = 18 + 0.75x$. Solving for $x$ gives $x = 24$.

Question 4

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Ming got a 19% raise in her salary from last year. This year she is earning $226,100. How much did she make last year?

Accepted Answer

Let X be the amount Ming earned last year. Her raise can be expressed as 0.19X. Therefore, her total salary for this year can be expressed as X + 0.19X = 1.19X. We know that this amount is $226,100, so we can set up the equation:
1.19X = $226,100
Solving for X, we get:
X = $190,000
Therefore, Ming earned $190,000 last year. Option A is the correct answer.

Question 5

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A couch sells for $1280. Instead of paying the total amount at the time of purchase, the same couch can be bought by paying $300 down and $90 a month for 12 months. How much is saved by paying the total amount at
The time of purchase?

Accepted Answer

The total cost when paying monthly is $300 down payment + ($90 * 12 months) = $300 + $1080 = $1380. The difference between paying all at once ($1280) and paying monthly ($1380) is $1380 - $1280 = $100. Therefore, $100 is saved by paying the total amount at the time of purchase.

Question 6

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Megan is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $190 for materials and equipment rental plus $55 per hour for labor. Company B gave and
Estimate of $260 for materials and equipment rental plus $45 per hour for labor. Determine how many hours of
Labor will be required for the two companies to cost the same.

Accepted Answer

Let $h$ be the number of hours of labor. The cost for Company A is $190 + 55h$, and the cost for Company B is $260 + 45h$. Setting these equal to each other to find when the costs are the same gives $190 + 55h = 260 + 45h$. Solving this equation for $h$ gives $h = 7$.

Question 7

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Seven more than five times a number is that number increased by 35.

Accepted Answer

Let x be the number. 
The equation is 5x + 7 = x + 35. 
Simplifying it, we get 4x = 28. 
Solving for x, we get x = 7. Therefore, the number is 7. The equation that can be set up is: 5x + 7 = x + 35
To solve for x: 
1. Subtract x from both sides: 5x + 7 - x = x + 35 - x 
4x + 7 = 35 
2. Subtract 7 from both sides: 4x + 7 - 7 = 35 - 7 
4x = 28 
3. Divide both sides by 4: 
x = 7 
Therefore, the answer is choice C, which states that the equation is 5x + 7 = x + 35, and the solution for x is 7.

Question 8

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-You inherit $10,000 with the stipulation that for the first year the money must be invested in two stocks paying 6% and 11% annual interest, respectively. How much should be invested at each rate if the total interest earned
For the year is to be $700?

Accepted Answer

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Question 9

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A car rental agency advertised renting a luxury, full-size car for $29.95 per day and $0.19 per mile. If you rent this car for 3 days, how many whole miles can you drive if you only have $200 to spend.

Accepted Answer

The total cost is the sum of the daily rental cost and the cost per mile. For 3 days, the rental cost is 3 * $29.95 = $89.85. If you have $200 to spend, the amount left for miles is $200 - $89.85 = $110.15. At $0.19 per mile, the number of miles you can drive is $110.15 / $0.19 ≈ 579 miles.

Question 10

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Mary and her brother John collect foreign coins. Mary has four times the number of coins that John has. Together they have 175 foreign coins. Find how many coins Mary has.

Accepted Answer

Let's use the variable "x" to represent the number of coins John has. According to the problem, Mary has four times the number of coins John has, which can be represented as 4x.

Together, they have 175 coins, so we can set up the equation:

x + 4x = 175

Simplifying this equation, we get:

5x = 175

Dividing both sides by 5, we get:

x = 35

This means that John has 35 coins. To find how many coins Mary has, we can substitute this value into the expression we came up with earlier:

4x = 4(35) = 140

So Mary has 140 coins.

Therefore, the best choice is B. Let's say John has x coins. Mary has four times as many coins as John, so she has 4x coins. Together they have 175 coins, so we can set up the equation:
x + 4x = 175
Simplifying the equation, we get:
5x = 175
Dividing both sides by 5, we get:
x = 35
So John has 35 coins. Mary has four times as many, so she has:
4x = 4(35) = 140
Therefore, Mary has 140 coins, making Choice B the correct answer.

Question 11

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Seven times a number is 18 more than three times that number.

Accepted Answer

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Question 12

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $62 under this promotional deal, how many minutes of phone calls did he make? Round to
The nearest integer, if necessary.

Accepted Answer

The equation to represent the situation is $15 + $0.05x = $62, where x is the number of minutes. Solving for x gives x = ($62 - $15) / $0.05 = 940 minutes.

Question 13

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A 12-ft. board is cut into 2 pieces so that one piece is 4 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

Accepted Answer

Let the length of the shorter piece be x. Then the length of the longer piece is 3x+4. The sum of the lengths of the two pieces is equal to the length of the original board, which is 12 feet. 
So, we can write the equation: 
x + (3x+4) = 12 
Simplifying and solving for x, we get: 
4x + 4 = 12 
4x = 8 
x = 2 
Therefore, the length of the shorter piece is 2 feet and the length of the longer piece is 3x+4 = 10 feet. 
So, the answer is B. Let x be the length of the shorter piece.
Then the longer piece is 3x+4.
The sum of the two pieces is 12 feet.
So, x + (3x+4) = 12.
Solving for x, we get x=2.
Therefore, the lengths of the two pieces are 2 feet and 10 feet. This matches choice B.

Question 14

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-An accountant receives a salary of $270,775 per year. During the year, he plans to spend $97,000 on his mortgage, $52,000 on food, $39,000 on clothing, $45,000 on household expenses, and $29,000 on other expenses.
With the money that is left, he expects to buy as many shares of stock at $225 per share as possible. How many
Shares will he be able to buy?

Accepted Answer

Let's start by finding out how much money the accountant will spend in total.
Total expenses = $97,000 + $52,000 + $39,000 + $45,000 + $29,000 = $262,000

To find out how much money he will have left, we subtract his total expenses from his salary:
Remaining money = $270,775 - $262,000 = $8,775

Finally, to figure out how many shares of stock he can buy, we divide the remaining money by the cost per share:
Shares = $8,775 / $225 = 39 shares

Therefore, the best choice is C) 39 shares. Let X be the number of shares he can buy.
Total money spent = Mortgage + Food + Clothing + Household + Other expenses
Total money spent = $97,000 + $52,000 + $39,000 + $45,000 + $29,000 = $262,000
Money remaining = Salary - Total money spent
Money remaining = $270,775 - $262,000 = $8,775

Number of shares he can buy = Money remaining / Price per share
Number of shares he can buy = $8,775 / $225 = 39 shares

Therefore, the answer is C) 39 shares as this is the number of shares he can buy with the money remaining after all the expenses.

Question 15

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-When Milo got promoted at work, he received a 10% pay raise. He now earns $33,000 per year. What was his annual salary before his raise?

Accepted Answer

Let x be Milo's annual salary before his raise. Then, we can set up the equation:
x + 0.1x = 33000
Simplifying the left side, we get:
1.1x = 33000
Dividing both sides by 1.1, we get:
x = 30000
Therefore, Milo's annual salary before his raise was $30,000. The correct answer is choice C. Let x be Milo's annual salary before his raise.
His new salary is 10% more than his old salary, so:
x + 0.10x = 33,000
Simplify and solve for x:
1.10x = 33,000
x = 30,000
Therefore, Milo's annual salary before his raise was $30,000.

Question 16

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-An auto repair shop charged a customer $417 to repair a car. The bill listed $57 for parts and the remainder for labor. If the cost of labor is $45 per hour, how many hours of labor did it take to repair the car?

Accepted Answer

Let x be the number of hours of labor.
The total cost of labor is equal to the total cost of repair minus the cost of parts:
45x = 417 - 57
45x = 360
x = 8
Therefore, it took 8 hours of labor to repair the car, which is option D.

Question 17

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-Center City East Parking Garage has a capacity of 251 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1227 cars, find the capacity for each garage.

Accepted Answer

Let x be the capacity of Center City West Parking Garage.
Then the capacity of Center City East Parking Garage is x + 251.
The combined capacity for the two garages is x + (x + 251) = 2x + 251 = 1227.
Solving for x, we get x = 488.
Therefore, the capacity of Center City West Parking Garage is 488 cars and the capacity of Center City East Parking Garage is 739 cars. Choice B matches this solution. Let x be the capacity of Center City West Parking Garage. Then the capacity of Center City East Parking Garage is x + 251. The combined capacity is 1227, so we can set up the equation x + x + 251 = 1227 and solve for x: 2x + 251 = 1227, 2x = 976, x = 488. Therefore, the capacity of Center City West Parking Garage is 488 cars and the capacity of Center City East Parking Garage is 739 cars (488 + 251). So the best choice is B.

Question 18

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-After a 14% price reduction, a boat sold for $21,500. What was the boat's price before the reduction? (Round to the nearest cent, if necessary.)

Accepted Answer

Let the original price of the boat be $x$. After a 14% reduction, the boat sells for 86% of its original price, so $0.86x = 21,500$. Solving for $x$ gives $x = 21,500 / 0.86 = 25,000$.

Question 19

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-A car rental agency charges $200 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $425?

Accepted Answer

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

Question 20

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked.
-You inherit $70,000 from a very wealthy grandparent, with the stipulation that for the first year, the money must be invested in two stocks paying 4% and 10% annual interest, respectively. How much should be invested
At each rate if the total interest earned for the year is to be $4000?

Accepted Answer

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

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. -Inclusive of a 7.5% sales tax, a diamond ring sold for $2042.50. Find the price of the ring before the tax was added. (Round to the nearest cent, if necessary.)

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -During an intramural basketball game, Team A scored 16 fewer points than Team B. Together, both teams scored a total of 150 points. How many points did Team A score during the game?

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -Ming got a 19% raise in her salary from last year. This year she is earning $226,100. How much did she make last year?

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -Seven more than five times a number is that number increased by 35.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -Mary and her brother John collect foreign coins. Mary has four times the number of coins that John has. Together they have 175 foreign coins. Find how many coins Mary has.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -Seven times a number is 18 more than three times that number.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -A 12-ft. board is cut into 2 pieces so that one piece is 4 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -When Milo got promoted at work, he received a 10% pay raise. He now earns $33,000 per year. What was his annual salary before his raise?

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -After a 14% price reduction, a boat sold for $21,500. What was the boat's price before the reduction? (Round to the nearest cent, if necessary.)

Set up an equation that can be used to solve the problem. Solve the equation and answer the question asked. -A car rental agency charges $200 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $425?