Question 1

Find the cost per ounce of a sunscreen made from 20 oz of a lotion that costs $2.25 per ounce and 50 oz of a lotion that costs $3.55 per ounce.

Accepted Answer

To find the cost per ounce of the sunscreen, we need to first find the total cost of the lotions used.

The cost of the first lotion (20 oz at $2.25 per oz) is:

20 oz x $2.25/oz = $45

The cost of the second lotion (50 oz at $3.55 per oz) is:

50 oz x $3.55/oz = $177.50

The total cost of the two lotions is:

$45 + $177.50 = $222.50

To find the cost per ounce, we divide the total cost by the total number of ounces:

$222.50 / (20 oz + 50 oz) = $222.50 / 70 oz = $3.18/oz

Therefore, the cost per ounce of the sunscreen is $3.18/oz, so the best choice is B.

Question 2

The sum of three consecutive odd numbers is 51. Find the first number.

Accepted Answer

Let x be the first odd number, then the next two consecutive odd numbers are x+2 and x+4.
According to the problem, we have:
x + (x+2) + (x+4) = 51
Simplifying the left-hand side, we get:
3x + 6 = 51
Subtracting 6 from both sides, we get:
3x = 45
Dividing both sides by 3, we get:
x = 15
Therefore, the first odd number is 15, which is answer choice C.

Question 3

A motorboat leaves a harbor and travels at an average speed of 12 mph towards a small island. Two hours later, a cabin cruiser leaves the same harbor at an average speed of 24 mph toward the same island. In how many hours after the cabin cruiser leaves the harbor will it be alongside the motorboat?

Accepted Answer

Let's call the time it takes for the cabin cruiser to catch up to the motorboat "t" (in hours).

The motorboat has a head start of 12 mph x 2 hours = 24 miles.

In that time, the motorboat has traveled 12 mph x 2 hours = 24 miles.

Now, let's set up an equation to solve for "t":

Distance traveled by motorboat = Distance traveled by cabin cruiser
12t + 24 = 24t

Simplifying the equation, we get:
24 = 12t
t = 2

Therefore, it will take the cabin cruiser 2 hours to catch up to the motorboat.

Answer: C

Question 4

The difference between a number and sixteen is eight. Find the number.

Accepted Answer

The answer of The difference between a number and sixteen...

Question 5

Three times the difference between five times a number and three is ninety-six. Find the number.

Accepted Answer

Let's start by setting up the equation:
3(5x - 3) = 96
Simplify and solve for x:
15x - 9 = 96
15x = 105
x = 7

Therefore, the answer is choice C, 7.

Question 6

Two small planes start from the same point and fly in opposite directions. The first plane is flying 55 mph slower than the second plane. In 2 h, the planes are 510 mi apart. Find the rate of the faster plane.

Accepted Answer

The combined speed of both planes is 510 miles / 2 hours = 255 mph. Let the speed of the faster plane be x mph. Then the slower plane's speed is x - 55 mph. So, x + (x - 55) = 255. Solving for x gives x = 155 mph.

Question 7

A union charges monthly dues of $4.24 plus $0.13 for each hour worked during a month. A union member's dues for March were $25.56. How many hours did the union member work during the month of March?

Accepted Answer

The union member's dues for March were $25.56. So, the total amount of dues paid is $25.56 - $4.24 = $21.32. Since the union member pays $0.13 for each hour worked during a month, the number of hours worked is $21.32 / $0.13 = 164 hours.

Question 8

One third of a number is negative twelve. Find the number.

Accepted Answer

To find the number, you multiply negative twelve by three (since one third of the number is negative twelve), resulting in -36.

Question 9

How many ounces of pure bran flakes must be added to 90 oz of cereal that is 46% bran flakes to produce a mixture that is 51.4% bran flakes?

Accepted Answer

The answer of How many ounces of pure bran flakes...

Question 10

An isosceles triangle has two sides of equal length. The length of the third side is 2 ft less than twice the length of an equal side. Find the length of the third side when the perimeter is 26 ft.

Accepted Answer

Let the length of each equal side be x. Then the third side is 2x - 2. The perimeter is x + x + (2x - 2) = 26. Solving for x gives x = 7. Therefore, the third side is 2(7) - 2 = 12 ft.

Question 11

A tea that is 18% jasmine is blended with a tea that is 12% jasmine. How many pounds of the 18% jasmine tea are used to make 10 lb of tea that is 13.8% jasmine?

Accepted Answer

To find the amount of 18% jasmine tea used, set up the equation: 0.18x + 0.12(10-x) = 0.138(10). Solving for x gives x = 3 lb.

Question 12

Find two consecutive even integers such that twelve times the first equals eight times the second. Find the smaller number.

Accepted Answer

The answer of Find two consecutive even integers such that...

Question 13

Ten cups of a restaurant's house Italian dressing is made up by blending olive oil costing $1.30 per cup with vinegar that costs $0.25 per cup. How many cups of vinegar are used if the cost of the blend is $0.78 per cup?

Accepted Answer

The cost of the blend per cup ($0.78) is a weighted average of the costs of olive oil ($1.30 per cup) and vinegar ($0.25 per cup). Let $x$ be the number of cups of vinegar. Then, the number of cups of olive oil is $10 - x$. The total cost of the blend is $10 \times 0.78 = 7.8$. Setting up the equation for the total cost: $1.30(10 - x) + 0.25x = 7.8$. Solving for $x$ gives $x = 5$, meaning 5 cups of vinegar are used.

Question 14

Forty ounces of a 25% gold alloy are mixed with 60 oz of a 20% alloy. Find the concentration of the resulting gold alloy.

Accepted Answer

The answer of Forty ounces of a 25% gold alloy...

Question 15

An adult and a child are on a seesaw 14.5 ft long. The adult weighs 152 lb and the child weighs 80 lb. How many feet from the child must the fulcrum be placed so that the seesaw balances?
Use the lever system equation  where d is the length of the lever and x is the distance of the fulcrum from the child.

Accepted Answer

The answer of An adult and a child are on...

Question 16

Two more than three times a number is eight. Find the number.

Accepted Answer

The answer of Two more than three times a number...

Question 17

The sum of two numbers is twenty. Three times the smaller number is equal to two times the larger number. Find the smaller number.

Accepted Answer

Let's call the smaller number "x" and the larger number "y". 
From the first sentence, we know that: 
x + y = 20 
From the second sentence, we know that: 
3x = 2y 
We can use substitution to solve for one of the variables. 
Rearranging the second equation: 
y = (3/2)x 
Now we can substitute this value for y in the first equation: 
x + (3/2)x = 20 
Combining like terms: 
(5/2)x = 20 
Multiplying both sides by (2/5): 
x = 8 
Therefore, the smaller number is 8.

Question 18

To determine the break-even point, or the number of units that must be sold so that no profit or loss occurs, an economist uses the formula  where P is the selling price per unit, x is the number of units that must be sold to break even, C is the cost to make each unit, and F is the fixed cost. A business analyst has determined that the selling price for a laser printer is $1800. The cost to make one laser printer is $960, and the fixed cost is $289,800.
Find the break-even point.

Accepted Answer

The answer of To determine the break-even point, or the...

Question 19

The sum of twice a number and six is eighteen. Find the number.

Accepted Answer

The equation based on the given statement is 2x + 6 = 18. Solving for x, we subtract 6 from both sides to get 2x = 12, and then divide by 2 to find x = 6.

Question 20

An herbalist has 20 oz of herbs costing $2.10 per ounce. How many ounces of herbs costing $1 per ounce should be mixed with the 20 oz to produce a mixture costing $1.44 per ounce?

Accepted Answer

Let x be the number of ounces of herbs costing $1 per ounce to be added to the mixture.

We can write an equation based on the information given:

20(2.10) + x(1) = (20 + x)(1.44)

Simplifying this equation, we get:

42 + x = 28.8 + 1.44x

Subtracting x and 28.8 from both sides, we get:

13.2 = 0.44x

Solving for x, we get:

x = 30

Therefore, 30 oz of herbs costing $1 per ounce should be mixed with the 20 oz to produce a mixture costing $1.44 per ounce.

Quiz 2: First-Degree Equations and Inequalities