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Linear Equations in One Variable

SAT Math· difficulty 4/5

The sum of two ages is 5050. In 1010 years the older will be 1.51.5 times the younger. How old is the older now?

  • A

    20

  • B

    32

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  • C

    30

  • D

    25

Explanation

Let younger yy, older 50−y50 - y. Then (50−y+10)=1.5(y+10)(50 - y + 10) = 1.5(y + 10). So 60−y=1.5y+1560 - y = 1.5y + 15, giving 45=2.5y45 = 2.5y and y=18y = 18. Older =50−18=32= 50 - 18 = 32.

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