Question 1

Solve the problem.
-An auto repair shop charged a customer $532 to repair a car. The bill listed $92 for parts and the remainderfor labor. If the cost of labor is $55 per hour, how many hours of labor did it take to repair the car?
A)8 hr
B)7 hr
C)9 hr
D)8.5 hr

Accepted Answer

The total cost was $532, with $92 for parts, leaving $440 for labor. At $55 per hour, it took $440 / $55 = 8 hours of labor.

Question 2

Solve the equation. The letters a, b, and c are constants.
-ax - b = c, a 
A) 
B) 
C) 
D)

Accepted Answer

To solve for x, we first need to isolate x on one side of the equation. Adding b to both sides, we get ax = b + c. Then, dividing both sides by a, we get x = (b + c)/a. Therefore, the answer is A.

Question 3

Solve the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the equation.
-
A) 
B) 
C) 
D) ...

Question 4

Solve the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the equation.
-
A) 
B) 
C) 
D) ...

Question 5

Solve the problem.
-Center City East Parking Garage has a capacity of 253 cars more than Center City West Parking Garage. Ifthe combined capacity for the two garages is 1,223 cars, find the capacity for each garage.
A)Center City East: 738 cars Center City West: 485 cars
B)Center City East: 485 cars Center City West: 738 cars
C)Center City East: 748 cars Center City West: 475 cars
D)Center City East: 475 cars Center City West: 748 cars

Accepted Answer

Let the capacity of Center City West Parking Garage be x. Then, the capacity of Center City East Parking Garage is x + 253. The combined capacity is x + (x + 253) = 1,223. Solving for x gives x = 485 for West and x + 253 = 738 for East.

Question 6

Solve the formula for the indicated variable.
-PV = nRT for T
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the formula for the indicated variable.
-PV...

Question 7

Solve the problem.
-It costs $19 per hour plus a flat fee of $32 for a plumber to make a house call. After writing an equation forthis situation, suppose the total cost to have a plumber come to a house is $203. How many hours did theplumber work?
A)9 hr
B)5 hr
C)20 hr
D)16 hr

Accepted Answer

The total cost is calculated by the equation: Total Cost = $19 * hours + $32. Given the total cost is $203, we solve for hours: $203 = $19 * hours + $32. Subtracting $32 from both sides gives $171 = $19 * hours. Dividing both sides by $19 gives hours = 9.

Question 8

Solve the problem.
-During an intramural basketball game, Team A scored 16 fewer points than Team B. Together, both teamsscored a total of 148 points. How many points did Team A score during the game?
A)66 points
B)82 points
C)67 points
D)74 points

Accepted Answer

Let the points scored by Team B be $x$. Therefore, Team A scored $x - 16$. Together, they scored $x + (x - 16) = 148$. Solving for $x$ gives $2x - 16 = 148$, so $2x = 164$, and $x = 82$. Thus, Team A scored $82 - 16 = 66$ points.

Question 9

Solve the problem.
-Mary and her brother John collect foreign coins. Mary has twice the number of coins that John has.Together they have 135 foreign coins. Find how many coins Mary has.
A)90 coins
B)45 coins
C)18 coins
D)81 coins

Accepted Answer

Mary has twice the number of coins that John has, so if John has x coins, Mary has 2x coins. Together, they have x + 2x = 3x coins, which equals 135. Solving 3x = 135 gives x = 45 (John's coins), so Mary has 2x = 90 coins.

Question 10

Solve the formula for the indicated variable.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the formula for the indicated variable.
-
A)...

Question 11

Solve the formula for the indicated variable.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the formula for the indicated variable.
-
A)...

Question 12

Solve the formula for the indicated variable.
-
A) 
B) 
C)P 
D)

Accepted Answer

The answer of Solve the formula for the indicated variable.
-
A)...

Question 13

Solve the equation. The letters a, b, and c are constants.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the equation. The letters a, b,...

Question 14

Solve the equation. The letters a, b, and c are constants.
-
A) 
B)x = abc
C) 
D)

Accepted Answer

The answer of Solve the equation. The letters a, b,...

Question 15

Solve the problem.
-Going into the final exam, which will count as three tests, Jerome has test scores of 61, 72, 59, 75, and 77.What score does Jerome need on the final in order to earn a C, which requires an average of 70?
A)72
B)75
C)70
D)79

Accepted Answer

Jerome currently has a total of 61 + 72 + 59 + 75 + 77 = 344 points from the five tests. In order to average 70, he needs a total of 70 x 6 = 420 points.

Since the final exam counts as three tests, it will be worth 3/6 or 1/2 of his total grade.

Let x be the score that Jerome needs on the final exam. Then:

(344 + x) / 6 = 70

Solving for x, we get:

x = 72

Therefore, Jerome needs to score a 72 on the final exam to earn a C.

Question 16

Solve the problem.
-A rectangular carpet has a perimeter of 194 inches. The length of the carpet is 51 inches more than thewidth. What are the dimensions of the carpet?
A)74 in. by 23 in.
B)74 in. by 97 in.
C)60 in. by 83 in.
D)85.5 in. by 97 in.

Accepted Answer

The perimeter of a rectangle is given by the formula $P = 2l + 2w$, where $l$ is the length and $w$ is the width. Given that the length is 51 inches more than the width, we can express the length as $l = w + 51$. Substituting this into the perimeter formula gives $194 = 2(w + 51) + 2w$. Simplifying, we get $194 = 4w + 102$, which further simplifies to $92 = 2w$, leading to $w = 46$ inches for the width. The length is $46 + 51 = 97$ inches. Therefore, the dimensions are 97 inches by 46 inches, which after checking the options, corresponds to the dimensions being doubled in option A, making it 74 inches by 23 inches due to a mistake in my calculation. Correcting this, the actual dimensions calculated don't directly match any of the options provided, indicating a mistake in my explanation regarding the final step of matching the dimensions to the options. The correct approach should have led to recognizing that none of the options directly match the calculated dimensions of 97 inches by 46 inches, suggesting a need to re-evaluate the calculation or the interpretation of the options.

Question 17

Solve the problem.
-Inclusive of a 6.3% sales tax, a diamond ring sold for $3,082.70. Find the price of the ring before the taxwas added. (Round to the nearest cent, if necessary.)
A)$2,900
B)$3,276.91
C)$2,888.49
D)$194.21

Accepted Answer

The total cost of the ring including the sales tax is $3,082.70. To find the original price before tax, divide the total cost by 1 plus the tax rate (expressed as a decimal). The tax rate is 6.3%, or 0.063 as a decimal. So, the original price is $3,082.70 / (1 + 0.063) = $3,082.70 / 1.063 ≈ $2,900.

Question 18

Solve the formula for the indicated variable.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the formula for the indicated variable.
-
A)...

Question 19

Solve the equation.
-
A){-13}
B){13}
C){5}
D){52}

Accepted Answer

The answer of Solve the equation.
-
A){-13}
B){13}
C){5}
D){52}...

Question 20

Solve the problem.
-After a 13% price reduction, a boat sold for $25,230. What was the boatʹs price before the reduction?(Round to the nearest cent, if necessary.)
A)$29,000
B)$3,279.90
C)$194,076.92
D)$28,509.90

Accepted Answer

The boat's price before the reduction can be found by dividing the sale price by the percentage it represents after the reduction, which is 100% - 13% = 87%. So, $25,230 / 0.87 = $29,000.

Quiz 1: Equations and Inequalities

Solve the problem. -An auto repair shop charged a customer $532 to repair a car. The bill listed $92 for parts and the remainderfor labor. If the cost of labor is $55 per hour, how many hours of labor did it take to repair the car?

Solve the equation. The letters a, b, and c are constants. -ax - b = c, a

Solve the equation. -

Solve the equation. -

Solve the problem. -Center City East Parking Garage has a capacity of 253 cars more than Center City West Parking Garage. Ifthe combined capacity for the two garages is 1,223 cars, find the capacity for each garage.

Solve the formula for the indicated variable. -PV = nRT for T

Solve the problem. -It costs $19 per hour plus a flat fee of $32 for a plumber to make a house call. After writing an equation forthis situation, suppose the total cost to have a plumber come to a house is $203. How many hours did theplumber work?

Solve the problem. -During an intramural basketball game, Team A scored 16 fewer points than Team B. Together, both teamsscored a total of 148 points. How many points did Team A score during the game?

Solve the problem. -Mary and her brother John collect foreign coins. Mary has twice the number of coins that John has.Together they have 135 foreign coins. Find how many coins Mary has.

Solve the formula for the indicated variable. -

Solve the formula for the indicated variable. -

Solve the formula for the indicated variable. -

Solve the equation. The letters a, b, and c are constants. -

Solve the equation. The letters a, b, and c are constants. -

Solve the problem. -Going into the final exam, which will count as three tests, Jerome has test scores of 61, 72, 59, 75, and 77.What score does Jerome need on the final in order to earn a C, which requires an average of 70?

Solve the problem. -A rectangular carpet has a perimeter of 194 inches. The length of the carpet is 51 inches more than thewidth. What are the dimensions of the carpet?

Solve the problem. -Inclusive of a 6.3% sales tax, a diamond ring sold for $3,082.70. Find the price of the ring before the taxwas added. (Round to the nearest cent, if necessary.)

Solve the formula for the indicated variable. -

Solve the equation. -

Solve the problem. -After a 13% price reduction, a boat sold for $25,230. What was the boatʹs price before the reduction?(Round to the nearest cent, if necessary.)