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Liam is buying balloons for his best friend’s birthday. He decides to buy x small balloons for $0.97 each and y large balloons for $1.32, after taxes. If Liam purchased a total of 16 balloons and spent a total of $17.62, which of the following systems of equations is true?(A) x = 11      y = 5(B) x + y = 16      1.32x + 0.97y = 17.62(C) x + 16 = y      0.97x + 1.32y = 17.62(D) x + 16 = y      1.32x + 0.97y = 17.62(E) x + y = 16      0.97x + 1.32y = 17.62

Question

Liam is buying balloons for his best friend’s birthday. He decides to buy x small balloons for 0.97eachandylargeballoonsfor0.97 each and y large balloons for 1.32, after taxes. If Liam purchased a total of 16 balloons and spent a total of $17.62, which of the following systems of equations is true?(A) x = 11      y = 5(B) x + y = 16      1.32x + 0.97y = 17.62(C) x + 16 = y      0.97x + 1.32y = 17.62(D) x + 16 = y      1.32x + 0.97y = 17.62(E) x + y = 16      0.97x + 1.32y = 17.62

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Solution

The correct system of equations that represents the problem is (B) x + y = 16 and 0.97x + 1.32y = 17.62.

This is because the first equation represents the total number of balloons Liam bought, which is 16. The second equation represents the total cost of the balloons, with x being the number of small balloons at 0.97eachandybeingthenumberoflargeballoonsat0.97 each and y being the number of large balloons at 1.

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