Julie started with 20 pieces of gum and gave away x pieces. Conrad started with 35 pieces of gum and gave away twice as many pieces as Julie did.

Question

How many pieces of gum did Julie give away if they had the same number of pieces of gum left?

Question 1 options:

A. 18

B. 5

C. 15

D. 8

Question 2 (1 point) 
Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of 1.2 gallons per minute.

Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of 0.8 gallon per minute.

After how many minutes will both aquariums contain the same amount of water?

Question 2 options:

148 Minutes

125 Minutes

25 Minutes

50 Minutes

Question 3 (1 point) 
Jerry has a new job and earns a salary of $45,000. Victoria has a new job and earns a salary of $54,000. Jerry will receive a salary increase of $2,500 per year, and Victoria will receive a salary increase of $1,500 per year.

Which equation can be used to find x, the number of years it will take Jerry to earn the same salary as Victoria?

Question 3 options:

45,000x + 2,500x = 54,000x + 1,500x

45,000x + 2,500 = 54,000x + 1,500

45,000 + 2,500x = 54,000 + 1,500x

45,000x + 2,500x = 54,000x + 1,500

GPT 3.5 · Answer

The correct answers are:

Question 1: To find the number of pieces of gum Julie gave away, we need to set up an equation. Julie started with 20 - x pieces of gum left, and Conrad started with 35 - (2x) pieces of gum left. We are told that they have the same number of pieces of gum left, so we can set up the equation:
20 - x = 35 - (2x)
Simplifying, we get:
x = 15
Therefore, Julie gave away 15 pieces of gum.
The correct answer is C. 15.

Question 2: We need to set up an equation to find the number of minutes it will take for both aquariums to contain the same amount of water. Let t represent the number of minutes. The amount of water in Aquarium I after t minutes is 4.6 + 1.2t, and the amount of water in Aquarium II after t minutes is 54.6 - 0.8t. We can set up the equation:
4.6 + 1.2t = 54.6 - 0.8t
Simplifying, we get:
2t = 50
t = 25
Therefore, both aquariums contain the same amount of water after 25 minutes.
The correct answer is C. 25 Minutes.

Question 3: We need to set up an equation to find the number of years it will take for Jerry to earn the same salary as Victoria. Let x represent the number of years. Jerry's salary after x years is 45,000 + 2,500x, and Victoria's salary after x years is 54,000 + 1,500x. We can set up the equation:
45,000 + 2,500x = 54,000 + 1,500x
Simplifying, we get:
1,000x = 9,000
x = 9
Therefore, it will take Jerry 9 years to earn the same salary as Victoria.
The correct answer is C. 45,000 + 2,500x = 54,000 + 1,500x.