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.
How many pieces of gum did Julie give away if they had the same number of pieces of gum left?
Question 1 options:
18
5
15
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
The correct answers are:
Question 1: x = 10 (Julie gave away 10 pieces of gum)
Question 2: 50 Minutes (both aquariums will contain the same amount of water after 50 minutes)
Question 3: 45,000 + 2,500x = 54,000 + 1,500x (equation to find x, the number of years it will take Jerry to earn the same salary as Victoria)
For Question 1:
Let's assume that Julie gave away x pieces of gum.
Conrad gave away twice as many pieces as Julie, so he gave away 2x pieces of gum.
After giving away x pieces of gum, Julie has 20 - x pieces left.
After giving away 2x pieces of gum, Conrad has 35 - 2x pieces left.
We are given that Julie and Conrad have the same number of pieces of gum left, so we can set up the equation:
20 - x = 35 - 2x
Simplifying the equation:
20 + x = 35
x = 35 - 20
x = 15
Therefore, Julie gave away 15 pieces of gum.
To find the answer to each question, let's break down the information provided and solve the problems step by step:
Question 1: How many pieces of gum did Julie give away if they had the same number of pieces of gum left?
Let's say Julie gave away x pieces of gum. Conrad also gave away twice as many pieces as Julie did, so Conrad gave away 2x pieces of gum.
Julie started with 20 pieces of gum, and after giving away x pieces, she has 20 - x pieces left.
Conrad started with 35 pieces of gum, and after giving away 2x pieces, he has 35 - 2x pieces left.
We need to find the value of x when they both have the same number of pieces of gum left.
So, we set up the equation:
20 - x = 35 - 2x
To solve for x, we bring like terms together:
x - 2x = 35 - 20
-x = 15
Multiplying both sides by -1 to isolate x:
x = -15
Since it doesn't make sense to have a negative number of pieces of gum given away, we can infer that Julie didn't give away any pieces of gum. Therefore, the answer is 0.
Answer: Julie gave away 0 pieces of gum.
Question 2: After how many minutes will both aquariums contain the same amount of water?
The rate at which water is being filled in Aquarium I is 1.2 gallons per minute, and the rate at which water is being drained from Aquarium II is 0.8 gallons per minute.
We need to find the time it takes 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
The amount of water in Aquarium II after t minutes is: 54.6 - 0.8t
We need to find the value of t when both aquariums have the same amount of water.
So, 4.6 + 1.2t = 54.6 - 0.8t
To solve for t, we bring like terms together:
1.2t + 0.8t = 54.6 - 4.6
2t = 50
Dividing both sides by 2 to isolate t:
t = 25
The time it takes for both aquariums to contain the same amount of water is 25 minutes.
Answer: After 25 minutes, both aquariums will contain the same amount of water.
Question 3: Which equation can be used to find x, the number of years it will take Jerry to earn the same salary as Victoria?
Jerry's starting salary is $45,000, and he receives a salary increase of $2,500 per year.
Victoria's starting salary is $54,000, and she receives a salary increase of $1,500 per year.
We need to find the number of years it will take 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
Victoria's salary after x years is: 54,000 + 1,500x
We need to find the value of x when their salaries are equal.
So, we set up the equation:
45,000 + 2,500x = 54,000 + 1,500x
To solve for x, we bring like terms together:
2,500x - 1,500x = 54,000 - 45,000
1,000x = 9,000
Dividing both sides by 1,000 to isolate x:
x = 9
Therefore, the number of years it will take Jerry to earn the same salary as Victoria is 9 years.
Answer: The equation that can be used to find x is 45,000 + 2,500x = 54,000 + 1,500x.