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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 4andpostersoftamarinscost4 and posters of tamarins cost 10. Mrs. Roy bought 5 posters and spent $32. How many of each type of poster did she buy?

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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:

  1. S + T = 5 (since Mrs. Roy bought 5 posters in total)

  2. 4S + 10T = 32 (since sloth posters cost 4eachandtamarinposterscost4 each and tamarin 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.

This problem has been solved

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