M7MBA wrote: ↑Thu Jan 07, 2021 10:25 am
If Jake loses 8 pounds, he will weigh twice as much as his sister. Together they now weigh 278 pounds. What is Jake's present weight, in pounds?
(A) 131
(B) 135
(C) 139
(D) 147
(E) 188
Answer:
E
Source: Official Guide
Solution:
We let J = Jake’s current weight and S = Sister’s current weight, in pounds, and create the equations:
J – 8 = 2S
J = 2S + 8 (Equation 1)
and
J + S = 278 (Equation 2)
To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:
(2S + 8) + S = 278
3S = 270
S = 90
We now know that the sister weighs S = 90 pounds, and we can plug that value into either equation to determine J. Let’s plug 90 for S into equation 2:
J + 90 = 278
J = 188
Alternate Solution:
From the answer choices, we understand that Jake’s weight is an integer and since the sum of Jake and his sister’s weights is an integer, it follows that Jake’s sister’s weight is an integer, too. Since Jake’s weight is 8 less than twice that of his sister’s, Jake’s weight must be an even integer (if sister’s weight is n, then Jake’s weight is 2n - 8, which is always even). The only even number among the given answer choices is 188.
Answer: E
