Benjamin and Marus like to share stickers. If Benjamin gives 40 stickers to Marus, the ratio of Benjamin to Marus's stickers will be 1 : 5. If Benjamin gives 90 stickers to Marus, their ratio will be 1 : 9. How many stickers does Benjamin have?
Question
Benjamin and Marus like to share stickers. If Benjamin gives 40 stickers to Marus, the ratio of Benjamin to Marus's stickers will be 1 : 5. If Benjamin gives 90 stickers to Marus, their ratio will be 1 : 9. How many stickers does Benjamin have?
Solution
Let's denote the initial number of stickers that Benjamin has as B and the initial number of stickers that Marus has as M.
From the problem, we have two equations based on the ratios given:
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After Benjamin gives 40 stickers to Marus, the ratio of Benjamin to Marus's stickers is 1:5. This can be written as: (B - 40) / (M + 40) = 1/5.
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After Benjamin gives 90 stickers to Marus, the ratio of Benjamin to Marus's stickers is 1:9. This can be written as: (B - 90) / (M + 90) = 1/9.
Now we have a system of two equations, and we can solve it step by step.
First, let's multiply both sides of the first equation by 5 and both sides of the second equation by 9 to get rid of the fractions:
- 5(B - 40) = M + 40, which simplifies to 5B - M = 240.
- 9(B - 90) = M + 90, which simplifies to 9B - M = 810.
Now we have a system of two equations:
- 5B - M = 240
- 9B - M = 810
Subtract the first equation from the second to get: 4B = 570, so B = 570 / 4 = 142.5.
But the number of stickers must be an integer, so there seems to be a mistake in the problem as it leads to a non-integer number of stickers.
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