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:
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
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.
Question 1:
To find out how many pieces of gum Julie gave away, we need to set up an equation based on the information given.
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.
If they had the same number of pieces of gum left, that means the number of pieces Julie gave away is equal to the number of pieces Conrad gave away.
So, we have the equation: 20 - x = 35 - (2x)
Now, let's solve for x:
20 - x = 35 - 2x
x - 2x = 35 - 20
-x = 15
x = -15
However, since we can't have a negative number of pieces of gum given away, we discard this solution.
Therefore, Julie gave away 0 pieces of gum.
Answer: Julie gave away 0 pieces of gum.
Question 2:
To find out after how many minutes both aquariums will contain the same amount of water, we need to set up an equation based on the information given.
Aquarium I contains 4.6 gallons of water and is being filled at a rate of 1.2 gallons per minute.
Aquarium II contains 54.6 gallons of water and is being drained at a rate of 0.8 gallon per minute.
Let's represent the number of minutes with 't'.
The equation for the amount of water in each aquarium after t minutes is:
Aquarium I: 4.6 + 1.2t
Aquarium II: 54.6 - 0.8t
We want to find when the amount of water in both aquariums is equal, so we set them equal to each other:
4.6 + 1.2t = 54.6 - 0.8t
Let's solve for t:
1.2t + 0.8t = 54.6 - 4.6
2t = 50
t = 25
After 25 minutes, both aquariums will contain the same amount of water.
Answer: After 25 minutes, both aquariums will contain the same amount of water.
Question 3:
To find the number of years it will take Jerry to earn the same salary as Victoria, we need to set up an equation based on the information given.
Jerry earns a salary of $45,000 and receives a salary increase of $2,500 per year.
Victoria earns a salary of $54,000 and receives a salary increase of $1,500 per year.
Let's represent the number of years with 'x'.
The equation for Jerry's salary after x years is:
45,000 + 2,500x
The equation for Victoria's salary after x years is:
54,000 + 1,500x
We want to find when Jerry's salary is equal to Victoria's salary, so we set them equal to each other:
45,000 + 2,500x = 54,000 + 1,500x
Let's solve for x:
2,500x - 1,500x = 54,000 - 45,000
x = 9,000 / 1,000
x = 9
It will take Jerry 9 years to earn the same salary as Victoria.
Answer: It will take Jerry 9 years to earn the same salary as Victoria.
To solve these questions, we need to use basic algebraic equations.
Question 1:
Let's set up an equation to represent the number of pieces of gum each person has left after giving some away. Julie has 20 - x pieces left, and Conrad has 35 - 2x pieces left (since he gave away twice as many as Julie).
We are told that they have the same number of pieces left, so we can set up the equation:
20 - x = 35 - 2x
To solve for x, we can distribute the negative sign on the right side of the equation:
20 - x = 35 - 2x
20 - x + 2x = 35 - 2x + 2x
20 + x = 35
Now, subtract 20 from both sides of the equation:
20 + x - 20 = 35 - 20
x = 15
Therefore, Julie gave away 15 pieces of gum.
Question 2:
We want to find out after how many minutes both aquariums contain the same amount of water. We know that Aquarium I starts with 4.6 gallons and is being filled at a rate of 1.2 gallons per minute. Aquarium II starts with 54.6 gallons and is being drained at a rate of 0.8 gallons per minute.
To set up the equation, let's assume x represents the number of minutes passed.
Aquarium I would have 4.6 + 1.2x gallons of water.
Aquarium II would have 54.6 - 0.8x gallons of water.
We want the two amounts to be equal, so we can set up the equation:
4.6 + 1.2x = 54.6 - 0.8x
Now, let's solve for x:
Add 0.8x to both sides and subtract 4.6 from both sides of the equation:
4.6 + 1.2x + 0.8x = 54.6 - 0.8x + 0.8x - 4.6
2x + 4.6 = 54.6
Subtract 4.6 from both sides:
2x + 4.6 - 4.6 = 54.6 - 4.6
2x = 50
Divide both sides by 2:
2x/2 = 50/2
x = 25
Therefore, after 25 minutes, both aquariums will contain the same amount of water.
Question 3:
We want to find the number of years it will take Jerry to earn the same salary as Victoria. Jerry's salary starts at $45,000 and increases by $2,500 per year. Victoria's salary starts at $54,000 and increases by $1,500 per year.
Let's set up an equation to represent their salaries after x years. Jerry's salary can be represented as 45,000 + 2,500x, and Victoria's salary is 54,000 + 1,500x.
We want their salaries to be equal, so we can set up the equation:
45,000 + 2,500x = 54,000 + 1,500x
Now, let's solve for x:
Subtract 1,500x from both sides and subtract 45,000 from both sides of the equation:
45,000 + 2,500x - 1,500x = 54,000 + 1,500x - 1,500x - 45,000
1,000x = 9,000
Divide both sides by 1,000:
1,000x/1,000 = 9,000/1,000
x = 9
Therefore, it will take Jerry 9 years to earn the same salary as Victoria.
So the answers to the questions are:
Question 1: C. 15
Question 2: C. 25 Minutes
Question 3: C. 45,000 + 2,500x = 54,000 + 1,500x