GRE Math Algebra Practice Question with Explnation
The larger of two numbers exceeds twice the smaller number by 9. The sum of twice the larger and 5 times the smaller number is 74. If a is the smaller number, which equation below determines the correct value of a?
A) 5(2a + 9) + 2a = 74
B) 5(2a - 9) + 2a = 74
C) (4a + 9) + 5a = 74
D) 2(2a + 9) + 5a = 74
D) 2(2a - 9) + 5a = 74
Solution:
The correct answer is ( D ).
To solve this problem, first convert the information given into its mathematical equivalent, as follows (use b to represent the larger number):
The larger of two numbers exceeds twice the smaller number by 9:
b = 2a + 9
The sum of twice the larger and five times the smaller number is 74:
2b + 5a = 74
Now, simply substitute the value of b into the second equation in order to solve for a:
2(2a + 9) + 5a = 74
Thus the answer is (D).
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