John and Peter each had some erasers. John gave away 40% of his; Peter gave away 1/7 of his.

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ydubrovensky4

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John and Peter each had some erasers. John gave away 40% of his erasers and Peter gave away 1/7 of his. As a result, they had the same number of erasers. If Peter gave away 13 erasers, how many erasers did they have altogether at first?

In this case, I am trying to figure out how to solve the problem of John and Peter's erasers. I know that I need to use the information that John gave away 40% of his erasers and Peter gave away 1/7 of his, but I am not sure how to do that. I am also not sure how to use the information that Peter gave away 13 erasers.

I started out with this equation
0.6J = (7/7)P - 13
 
ydubrovensky4 said:
John and Peter each had some erasers. John gave away 40% of his erasers and Peter gave away 1/7 of his. As a result, they had the same number of erasers. If Peter gave away 13 erasers, how many erasers did they have altogether at first?

In this case, I am trying to figure out how to solve the problem of John and Peter's erasers. I know that I need to use the information that John gave away 40% of his erasers and Peter gave away 1/7 of his, but I am not sure how to do that. I am also not sure how to use the information that Peter gave away 13 erasers.

I started out with this equation
0.6J = (7/7)P - 13
Click to expand...

What are the definitions of "P" and "J"? What does your equation, 0.6J = P - 13, express?

Note that Peter gave away 13, which comprised 1/7 of his total. Then what was his total? (Hint: Multiply by 7.)

How many, then, did Peter end up with? (Hint: Subtract 13 from total.)

John, after giving away 40% of his stock, had the same number of erasers as does Peter. So how many does he have? (Hint: Copy.)

Since this amount is 60% of what he'd started with, then how many erasers comprise 10% of what he'd started with? (Hint: Divide by 6.)

Then how many did he have at the beginning? (Hint: Multiply by 10.)

Then how many did they have when they started? (Hint: Add.)
 
stapel said:
What are the definitions of "P" and "J"? What does your equation, 0.6J = P - 13, express?

Note that Peter gave away 13, which comprised 1/7 of his total. Then what was his total? (Hint: Multiply by 7.)

How many, then, did Peter end up with? (Hint: Subtract 13 from total.)

John, after giving away 40% of his stock, had the same number of erasers as does Peter. So how many does he have? (Hint: Copy.)

Since this amount is 60% of what he'd started with, then how many erasers comprise 10% of what he'd started with? (Hint: Divide by 6.)

Then how many did he have at the beginning? (Hint: Multiply by 10.)

Then how many did they have when they started? (Hint: Add.)
Click to expand...
P * 7 = 13 * 7
P = 91

P - 13 = 91 - 13
P = 78

J / 6 = 78 / 6
J / 6 = 13

13 * 10 = 130

130 + 91 = 221
 
ydubrovensky4 said:
John and Peter each had some erasers. John gave away 40% of his erasers and Peter gave away 1/7 of his. As a result, they had the same number of erasers. If Peter gave away 13 erasers, how many erasers did they have altogether at first?

In this case, I am trying to figure out how to solve the problem of John and Peter's erasers. I know that I need to use the information that John gave away 40% of his erasers and Peter gave away 1/7 of his, but I am not sure how to do that. I am also not sure how to use the information that Peter gave away 13 erasers.

I started out with this equation
0.6J = (7/7)P - 13
Click to expand...
I think you meant that 1-1/7 = 6/7, not 7/7. After all, 1- 0 = 7/7
 
For the record, you have the correct answer. My main concern is that the result of your math is not correct at all. For example P * 7 = 13 * 7 implies that P = 91. That's nonsense!
 
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