Simon and Jimmy had 167 stamps altogether. Simon gave 4/7 of his stamps to Trina, and Jimmy gave 37 stamps to Trina. Simon and Jimmy had the same number of stamps left. How many stamps did Jimmy have in the beginning?
I need you to show me how you did it because I have trouble with these types of questions.
using two variables:
original number of Simons stamps --- x
original number of Jimmy's stamps --- y
x+y = 167 or y = 167-x
after giveaway:
Simon had (3/7)x
Jimmy had (y-37)
--> it says, those two expressions are the same, so
3x/7 = y-37
times 7
3x = 7y - 259
3x - 7y = -259
subbing in the first equation:
3x - 7(167-x) = -259
3x - 1169 + 7x = -259
10x = 910
x = 91
y = 167-91 = 76
Jimmy had 76 stamps at the start.
Argghhh, just noticed that I answered this same question back in 2011
http://www.jiskha.com/display.cgi?id=1294093445
Let's solve this step by step:
1. Let's assume that Simon had x stamps in the beginning.
2. Jimmy had 167 - x stamps (since together they had 167 stamps).
3. Simon gave away (4/7) * x stamps to Trina.
4. After giving away the stamps, Simon had x - (4/7) * x = (7/7 - 4/7) * x = (3/7) * x stamps left.
5. Jimmy gave away 37 stamps to Trina, so he had (167 - x) - 37 = 130 - x stamps left.
6. According to the question, Simon and Jimmy had the same number of stamps left, so (3/7) * x = 130 - x.
7. We can now solve for x:
(3/7) * x + x = 130
(3x/7) + (7x/7) = 130
(10x/7) = 130
10x = 130 * 7
10x = 910
x = 910 / 10
x = 91
Therefore, Jimmy had 167 - x = 167 - 91 = 76 stamps in the beginning.
To solve this problem, we can set up an equation to represent the given information.
Let's assume that Jimmy had x stamps in the beginning.
Simon gave 4/7 of his stamps to Trina, so he gave away (4/7) * x stamps.
After giving away his stamps, Simon is left with x - (4/7) * x stamps.
Jimmy gave away 37 stamps, so he is left with x - 37 stamps.
According to the problem, Simon and Jimmy had the same number of stamps left, so we can set up the equation:
x - (4/7) * x = x - 37
To solve this equation, we can simplify both sides:
(7/7)x - (4/7) * x = (7/7)x - 37
(3/7)x = 37
Next, we can isolate x by multiplying both sides of the equation by (7/3):
(7/3) * (3/7)x = (7/3) * 37
x = 7 * 37 / 3
Using the calculator, we can compute the value of x:
x = 259 / 3
x ≈ 86.333
Therefore, Jimmy had approximately 86 stamps in the beginning.