SAT Math Multiple Choice Practice Question 6: Answer and Explanation

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Question: 6

6. The ratio of Dora's money to Lisa's money is 7:5. If Dora has $24 more than Lisa, how much does Dora have?

A. $10
B. $14
C. $60
D. $84
E. $144

Correct Answer: D

Explanation:

D. Don't let this one fool you. Thinking that the girls have $24 combined is tempting, but that's not what the problem says. To do this problem, you need to find two numbers in the ratio 7:5 that have a difference of 24. You can work this problem a couple of ways. One is to use algebra: You can call Dora's money 7x and Lisa's money 5x. Then you can say that 7x = 5x + 24, or 7x - 5x = 24. Thus, 2x = 24, and x = 12. Plugging 12 back into the original equation (always an important step) tells you that Lisa's money is 5(12) = $60, and Dora's is 7(12) = $84. The other way to solve this problem is to subtract the numbers in the ratio instead of adding them. Because 7 - 5 = 2, and 2 goes into 24 12 times, you can multiply the original ratio numbers by 12, giving you the same answers you get using algebra.

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