James bought two shirts and three pairs of pants for 87 dollars Matthew bought two pairs of pants and one shirt for 53 dollars Assuming each pair of pants costs the same amount and each shirt costs the same amount, how much does one pair of pants cost?
Answer
A
the fraction with numerator the 2 by 2 matrix row 1, 2 87 row 2, 2 53 and denominator negative 4 is equal to 17 dollars
B
the fraction with numerator the 2 by 2 matrix row 1, 87 3 row 2, 53 1 and denominator negative 4 is equal to 18 dollars
C
the fraction with numerator the 2 by 2 matrix row 1, 87 3 row 2, 53 2 and denominator 1 is equal to 15 dollars
D
the fraction with numerator the 2 by 2 matrix row 1, 2 87 row 2, 1 53 and denominator 1 is equal to 19 dollars
Explanation
Let s be the cost of one shirt and p the cost of one pair of pants. The purchases give 2s + 3p = 87 and s + 2p = 53; doubling the second equation gives 2s + 4p = 106. Subtract the first equation to get p = 106 − 87 = 19, so one pair of pants costs 19 dollars, as stated in choice D.
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