Çözüldü Multivariable Linear Equations

A certain pet store sells only dogs and cats. In March, the store sold twice as many dogs as cats. In April, the store sold twice the number of dogs that it sold in March, and three times the number of cats that it sold in March. If the total number of pets the store sold in March and April combined was 500, how many dogs did the store sell in March?

A) 80
B) 100
C) 120
D) 160
E) 180

Number of dogs and cats sold in March and April are D1, C1, D2, C2 respectively.
D1 = 2C1
D2 = 2D1 = 2(2C1) = 4C1
C2 = 3C1
D1 + C1 + D2 + C2 = 500
2C1 + C1 + 4C1 + 3C1 = 500
10C1 = 500
C1 = 50
D1 = 2C1 = 2·50 = 100
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Original solution based on the choices:
Plug In the Answers, starting with the middle choice. If 120 dogs were sold in March, then 60 cats were sold that month. In April, 240 dogs were sold, along with 180 cats. The total number of dogs and cats sold during those two months is 600, which is too large, so eliminate (C), (D), and (E). Try (B). If there were 100 dogs sold in March, then 50 cats were sold; in April, 200 dogs were sold along with 150 cats. The correct answer is (B) because 100 + 50 + 200 + 150 = 500.
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