SOLUTION: Hi Jack and ayden had some stamps at first. After Jack gave ayden 60 stamps both had the same number of stamps. If ayden were to return 54 stamps to Jack the ratio of jacks stamps

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Question 1207689: Hi
Jack and ayden had some stamps at first. After Jack gave ayden 60 stamps both had the same number of stamps. If ayden were to return 54 stamps to Jack the ratio of jacks stamps to ayden would be 5 to 2.
How many stamps did Jack have at first.
Find the ratio of jacks to ayden stamps at first.
Answer by greenestamps(13195) About Me  (Show Source):
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Let x be the number of stamps each of them has after Jack gave Ayden 60 stamps. Then the number Jack started with was x+60, and the number Ayden started with was x-60.

After Ayden returned 54 stamps to Jack, the number Ayden had was x-54 and the number Jack had was x+54.

At that time, the ratio of the number Jack had to the number Ayden had was 5:2.

%28x%2B54%29%2F%28x-54%29=5%2F2
5%28x-54%29=2%28x%2B54%29
5x-270=2x%2B108
3x=378
x=378%2F3=126

The number of stamps Jack started with was x+60 = 126+60 = 186.
The number of stamps Ayden started with was x-60 = 126-60 = 66.

ANSWERS:
How many stamps did Jack have at first. 186
Find the ratio of jacks to ayden stamps at first. 186:66 = 31:11