In the last week, Todd has lost 12 pounds and now weighs exactly three times as much as his younger brother...

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BTGmoderatorLU: Moderator; Posts: 2558; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Oct 19, 2020 4:49 pm

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Source: Veritas Prep

In the last week, Todd has lost 12 pounds and now weighs exactly three times as much as his younger brother. Together they weigh 280 pounds. How much did Todd weigh a week ago, in pounds?

A. 210
B. 213
C. 220
D. 222
E. 225

The OA is D

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Source: Beat The GMAT — Problem Solving | Mon Oct 19, 2020 4:49 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: In the last week, Todd has lost 12 pounds and now weighs exactly three times as much as his younger brother...

by deloitte247 » Sun Oct 25, 2020 6:58 am

Let Todd's weight = t
Let his younger brother = b
t - 12 = 3b
t - 3b = 12 --- eqn (1)
(t - 12) + b = 280
t + b = 280 + 12 = 292
t + b = 292 --- eqn (2)
t = 292 - b --- eqn (3)
Substitute eqn (3) into eqn (1)
292 - b - 3b = 12
-4b = 12 - 292
-4b = - 280
$$b=\frac{-280}{-4}=70$$
t = 292 - 70 = 222

Answer = option D

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: In the last week, Todd has lost 12 pounds and now weighs exactly three times as much as his younger brother...

by Scott@TargetTestPrep » Tue Oct 27, 2020 9:10 am

BTGmoderatorLU wrote: ↑
Mon Oct 19, 2020 4:49 pm
Source: Veritas Prep

In the last week, Todd has lost 12 pounds and now weighs exactly three times as much as his younger brother. Together they weigh 280 pounds. How much did Todd weigh a week ago, in pounds?

A. 210
B. 213
C. 220
D. 222
E. 225

The OA is D

Solution:

We can let t = Todd’s old weight and b = his brother’s current weight.

We can create the following equations:

t - 12 = 3b

And

t - 12 + b = 280

Replacing t - 12 in the second equation by 3b, we have:

3b + b = 280

4b = 280

b = 70

Substitute b = 70 back into the very first equation, we have:

t - 12 = 3(70)

t = 222

Alternate Solution:

Let’s let x = brother’s current weight. This means that Todd’s current weight = 3x. We have:

x + 3x = 280

4x = 280

x = 70

Todd’s brother weighs 70 pounds, and Todd currently weighs (3)(70) = 210 pounds. Last week Todd weighed 12 more pounds, so last week he weighed 222 pounds.

Answer: D

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Founder and CEO
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