Question 1

A jeweler has priced a diamond ring at $500. This price represents $20 less than twice the cost of the ring to the jeweler. Find the cost of the ring to the jeweler.

Accepted Answer

Let's start by setting up an equation:

$500 = 2x - $20

where x is the cost of the ring to the jeweler.

We can solve for x:

$500 + $20 = 2x

$520 = 2x

$x = $260

Therefore, the cost of the ring to the jeweler is $260.

The answer is D.

Question 2

Michael bought 5 pizzas for a total of $32. What was the price per pizza?

Accepted Answer

To find the price per pizza, divide the total cost by the number of pizzas: $32 / 5 = $6.40.

Question 3

Solve the equation. 4 t + 3 = 15

Accepted Answer

The answer of Solve the equation. 4 t + 3...

Question 4

Jill worked 8 hours Saturday at $5.50 per hour. How much did she earn?

Accepted Answer

To find Jill's earnings, we need to multiply her hours worked by her hourly rate. 
8 hours x $5.50/hour = $44. Therefore, the correct answer is D) $44.

Question 5

Suppose that two items cost $50. If one of the items costs $20, what is the cost of the other item?

Accepted Answer

If two items cost $50, then one item costs $25. 
If one of the items costs $20, then the other item must cost $25 - $20 = $5.

Question 6

The rainfall in June was 6.6 inches. This was 2 inches less than twice the rainfall in July. Find the amount of rainfall in inches for July.

Accepted Answer

The problem can be solved by setting up the equation 6.6 = 2x - 2, where x is the rainfall in July. Solving for x gives x = 4.3, so the rainfall in July was 4.3 inches.

Question 7

Solve the equation. 21 $-$ s = 25

Accepted Answer

The answer of Solve the equation. 21 $-$ s =...

Question 8

Solve the equation. 3 y $-$ 14 = 7

Accepted Answer

The answer of Solve the equation. 3 y $-$ 14...

Question 9

Solve the equation. 8 = 4 b $-$ 8

Accepted Answer

The answer of Solve the equation. 8 = 4 b...

Question 10

A bill from the limousine company was $450. This included $100 for the service and $100 for each hour of use. Find the number of hours that the limousine was used.

Accepted Answer

The answer of A bill from the limousine company was...

Question 11

An executive is earning $150,000 per year. This is $14,000 less than twice her salary 7 years ago. Find her salary 7 years ago.

Accepted Answer

The answer of An executive is earning $150,000 per year....

Question 12

Solve the equation. $-$ 6 b + 2 = 20

Accepted Answer

The answer of Solve the equation. $-$ 6 b +...

Question 13

The length of a rectangular floor is 35 meters. This length is 5 meters less than four times the width of the floor. Find the width of the floor.

Accepted Answer

The width of the floor can be found by setting up the equation: Length = 4 * Width - 5. Substituting the given length (35 meters) into the equation gives 35 = 4 * Width - 5. Solving for Width, we add 5 to both sides to get 40 = 4 * Width, and then divide both sides by 4 to find that Width = 10 meters.

Question 14

Todd is on a 1,850-calorie-per-day diet plan. This plan permits 600 calories less than twice the number of calories permitted by Lerae's diet plan. How many calories are permitted by Lerae's plan?

Accepted Answer

Let x be the number of calories permitted by Lerae's plan. 
The problem states that Todd's plan permits 600 calories less than twice the number of calories permitted by Lerae's plan. So we can set up an equation: 
1850 = 2x - 600 
2450 = 2x 
x = 1225 
Therefore, Lerae's plan permits 1225 calories per day. The answer is C, 1,225 calories.

Question 15

If eight times a certain number is subtracted from 68, the result is 4. Find the number.

Accepted Answer

Let's call the certain number "x".

The problem states:

68 - 8x = 4

To solve for x, we need to isolate it on one side of the equation.

First, we can simplify the left side by subtracting 68 from both sides:

-8x = -64

Next, we can solve for x by dividing both sides by -8:

x = 8

Therefore, the certain number is 8, which is answer choice B.

Question 16

Tracy received a cell phone bill for $134.94. Included in the $134.94 was a charge of $39.99 for the monthly plan and a charge for 211 extra minutes. How much is Tracy being charged for each extra minute?

Accepted Answer

To find the cost per extra minute, subtract the monthly plan charge from the total bill and then divide by the number of extra minutes. ($134.94 - $39.99) / 211 = $0.45.

Question 17

If nine times a certain number is subtracted from 65, the result is 2. Find the number.

Accepted Answer

Let's call the certain number x. The problem tells us that if we subtract nine times x from 65, we get 2. In equation form, that is: 
65 - 9x = 2 
To solve for x, we need to isolate x on one side of the equation. We can start by subtracting 65 from both sides: 
-9x = -63 
Now we can divide both sides by -9 to get: 
x = 7 
So the certain number is 7, and the correct answer choice is C.

Question 18

Twelve added to a certain number is 25. What is the number?

Accepted Answer

The answer of Twelve added to a certain number is...

Question 19

Eleven years ago Rosa was 23 years old. Find Rosa's present age.

Accepted Answer

The answer of Eleven years ago Rosa was 23 years...

Question 20

Chris is following a 2,420-calorie-per-day diet plan. This plan permits 580 calories less than twice the number of calories permitted by Lerae's diet plan. How many calories are permitted by Lerae's plan?

Accepted Answer

To find the number of calories permitted by Lerae's plan, let x be the number of calories in Lerae's plan. According to the problem, Chris's plan allows 580 calories less than twice Lerae's calories: 2x - 580 = 2,420. Solving for x gives: 2x = 3,000, so x = 1,500.

Quiz 3: Equations, Inequalities and Problem Solving