Solving Systems of Equations in Word Problems - New SAT Math - No Calculator

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Question

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is years old?

Answer

Since Gary will be 37 in five years, he is years old now. He is twice as old as Cathy, so she is years old, and in five years, she will be years old.

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Question

Mark is three times as old as his son Brian. In ten years, Mark will be years old. In how many years will Mark be twice as old as Brian?

Answer

In ten years, Mark will be years old, so Mark is years old now, and Brian is one-third of this, or years old.

Let be the number of years in which Mark will be twice Brian's age. Then Brian will be , and Mark will be . Since Mark will be twice Brian's age, we can set up and solve the equation:

Mark will be twice Brian's age in years.

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