Problem Solving

BTGmoderatorLU wrote: ↑

Fri Jul 08, 2022 7:54 am

Source: GMAT Paper Tests

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. \(188\)

The OA is E

Here's a solution that uses one variable.

Let x = Jake's present weight in pounds
So, x - 8 = Jake's hypothetical weight IF he were to lose 8 pounds

If Jake loses 8 pounds, he will weigh twice as much as his sister.
In other words, the sister weighs HALF as much as Jake's hypothetical weight of x - 8 pounds
So, (x - 8)/2 = sister's present weight

Together they NOW weigh 278 pounds.
So, Jake's present weight + sister's present weight = 278
So, x + (x - 8)/2 = 278
Eliminate the fraction by multiplying both sides by 2 to get: 2x + (x - 8) = 556
Simplify: 3x - 8 = 556
Add 8 to both sides: 3x = 564
Solve: x = 564/3 = 188

Answer: E

BTGmoderatorLU wrote: ↑

Fri Jul 08, 2022 7:54 am

Source: GMAT Paper Tests

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. \(188\)

The OA is E

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

Answer: E