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In the last week, Todd has lost 12 pounds and now weighs exactly three

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In the last week, Todd has lost 12 pounds and now weighs exactly three [#permalink]

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New post 25 Jul 2017, 22:41
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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

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Re: In the last week, Todd has lost 12 pounds and now weighs exactly three [#permalink]

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New post 25 Jul 2017, 23:03
Answer is D

I solved this with answer choices given.

Going with D. Todd weigh 222 pounds a week ago. Now he has lost 12 pounds so current weight is 210 pounds
Todd and his younger brother weighs 280 pounds

210 + x =280 ..where x is younger brother's weight. solving we get x=70
Now Todd weighs three times as much as his younger brother

younger brother's weight x 3 = todd's current weight
70 x 3 =210.. it is match
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In the last week, Todd has lost 12 pounds and now weighs exactly three [#permalink]

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New post 25 Jul 2017, 23:04
Let Todd's weight be x and his brother's weight be y

From the question stem,
x - 12 = 3y => x - 3y = 12 -> 1
Also, since the sum of their weights is 280,
x - 12 + y = 280 => x + y = 292 -> 2

(1) - (2) gives -4y = -280 => y = 70
Therefore, x = 280 + 12 - 70 = 222(Option D)
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Re: In the last week, Todd has lost 12 pounds and now weighs exactly three [#permalink]

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New post 09 Aug 2017, 13:35
Bunuel wrote:
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


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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Re: In the last week, Todd has lost 12 pounds and now weighs exactly three   [#permalink] 09 Aug 2017, 13:35
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In the last week, Todd has lost 12 pounds and now weighs exactly three

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