SOLUTION: If Amy gives 10 of her stamps to Robin, she will have four times as many stamps as Robin. If she gives 20 of her stamps to Robin, she will have three times as many stamps as Robin.
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Question 1086083: If Amy gives 10 of her stamps to Robin, she will have four times as many stamps as Robin. If she gives 20 of her stamps to Robin, she will have three times as many stamps as Robin. How many stamps do they have in all?
First equation is
A - 10 = 4*(R+10). (1)
Second equation is
A - 20 = 3*(R+20). (2)
Simplify these equations:
A - 4R = 50, (3)
A - 3R = 80. (4)
To solve the system, distract eq(3) from eq(4) (both sides). You will get
-3R - (-4R) = 80 - 50, or
R = 30.
Answer. Robin has 30 stamps. Amy has 4*(30+10) + 10 = 170 stamps.
