Age Problem

Three times Alley's age plus twelve is equal to Sonya's age.
Two times Alley's age plus four times Sonya's age is 188. How old is Sonya?

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a = Alley's age
3a + 12 = Sonya's age   {three times Alley's age plus twelve equals Sonya's age}

2a + 4(3a + 12) = 188   {two times Alley's age plus four times Sonya's age is 188}
2a + 12a + 48 = 188   {used distributive property}
14a + 48 = 188   {combined like terms}
14a = 140   {subtracted 48 from each side}
a = 10   {divided each side by 14}
3a + 12 = 42   {substituted 10, in for a, into 3a + 12}

Sonya is 42

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