At the zoo gift shop, posters of sloths cost $4 and posters of tamarins cost $10. Mrs. Roy bought 5 posters and spent $32. How many of each type of poster did she buy?
Question
At the zoo gift shop, posters of sloths cost 10. Mrs. Roy bought 5 posters and spent $32. How many of each type of poster did she buy?
Solution
Let's denote the number of sloth posters as S and the number of tamarin posters as T.
From the problem, we have two equations:
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S + T = 5 (since Mrs. Roy bought 5 posters in total)
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4S + 10T = 32 (since sloth posters cost 10 each, and Mrs. Roy spent $32 in total)
We can solve these equations step by step:
First, multiply the first equation by 4 to make the coefficients of S the same in both equations:
4S + 4T = 20
Now, subtract this new equation from the second equation:
4S + 10T - (4S + 4T) = 32 - 20
This simplifies to:
6T = 12
Divide both sides by 6 to solve for T:
T = 2
Substitute T = 2 into the first equation:
S + 2 = 5
Subtract 2 from both sides to solve for S:
S = 3
So, Mrs. Roy bought 3 sloth posters and 2 tamarin posters.
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