weight problem

[sportypk]

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 188. how?

[DavidP]

x = weight of Jake's sister

2x + 8 = Jake's weight

278 = Jake's sister's weight + Jake's weight

278 = x + (2x + 8)

278 = 3x + 8

270 = 3x

x = 90

Thus, Jake's weight = 2x + 8 = 2*90 + 8 = 188

[egybs]

Even easier -

we know that

J-8 = 2S
Therefore S = (J-8 )/2

So J + .5J -4 = 278

(3/2)J = 282
J = 188

[sportypk]

wow i feel like the queen of silly mistakes...thanks guys...

[Scott@TargetTestPrep]

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 188. how?

Solution:

This problem can be solved as a simple word problem in which we must convert words to math. Before we create our equations, we want to define some variables.

J = Jake's current weight, in pounds

S = Sister's current weight, in pounds

We are told that "If Jake loses 8 pounds, he will weigh twice as much as his sister." We put this into an equation:

J - 8 = 2S

We can isolate J by adding 8 to 2S:

J = 2S + 8 (Equation 1)

Next, we are told that "Together they now weigh 278 pounds." We can also put this into an equation.

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

[Brent@GMATPrepNow]

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

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 fractions 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 = [spoiler]188 = E[/spoiler]

Cheers,
Brent

[GMATGuruNY]

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

ALWAYS KEEP YOUR EYE ON THE ANSWER CHOICES.

If Jake loses 8 pounds, he will weigh twice as much as his sister.
j-8 = 2s
j = 2s + 8 = even + even = even.

Since Jake's weight must be an EVEN VALUE, the correct answer is E.

[egybs]

GMAT 'experts', I still like my solution from 7 years ago better.

[Brent@GMATPrepNow]

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

ALWAYS KEEP YOUR EYE ON THE ANSWER CHOICES.

If Jake loses 8 pounds, he will weigh twice as much as his sister.
j-8 = 2s
j = 2s + 8 = even + even = even.

Since Jake's weight must be an EVEN VALUE, the correct answer is E.

Sweeeeeeeeeet!

Cheers,
Brent

[[email protected]]

Hi All,

The answer choices in this question are 'spread out' in such a way that we can get to the correct answer with just a bit of logical thinking.

We're told that the total weight of Jake and his sister = 278 pounds. We're also told that if Jake LOST 8 pounds, he would TWICE as much as his sister....

This means that Jake weighs MORE than twice his sister RIGHT NOW. Since the total is 278 pounds, Jake's weight MUST make up MOST of that total weight (a lot more than half). There's only one answer that fits....

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Brent@GMATPrepNow]

Hi All,

The answer choices in this question are 'spread out' in such a way that we can get to the correct answer with just a bit of logical thinking.

We're told that the total weight of Jake and his sister = 278 pounds. We're also told that if Jake LOST 8 pounds, he would TWICE as much as his sister....

This means that Jake weighs MORE than twice his sister RIGHT NOW. Since the total is 278 pounds, Jake's weight MUST make up MOST of that total weight (a lot more than half). There's only one answer that fits....

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Another sweeeeet answer!
And here I'm using algebra like some sucker!!

I love seeing how many approaches one can take with a GMAT math question!!!

I've already reached my exclamation mark quota for the day, so I hope no one else presents more awesome approaches.

Cheers,
Brent

[Ian Stewart]

Mitch's solution is obviously fastest, but there is a no-variable solution we can use if the answer choices don't allow for any trick: if Jake loses 8 pounds, then together they'll weigh 270 pounds, and if Jake would then weigh twice as much as his sister, the ratio of their weights is 2 to 1, so Jake would weigh 2/3 of 270, or 180 pounds. Add back the 8, and 188 is the answer.