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Samantha saved $100 in 5 weeks. Each week she saved $6 more than the

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Bunuel
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Samantha saved $100 in 5 weeks. Each week she saved $6 more than the [#permalink] New post   24 Mar 2022, 07:00
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Samantha saved $100 in 5 weeks. Each week she saved $6 more than the previous week. How much did she save in the first week?

A. $4
B. $8
C. $12
D. $16
E. $20
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B
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Re: Samantha saved $100 in 5 weeks. Each week she saved $6 more than the [#permalink] New post   24 Mar 2022, 07:20
Samantha saved $100 in 5 weeks. Each week she saved $6 more than the previous week. How much did she save in the first week?

A trick to solve such questions faster:

Samantha's savings in week 1 = x.
So consecutive weeks will be = x + 6, x + 12, etc.

However, we can also write it as follows (by taking the middle week as x):
Week 1 = x - 12
Week 2 = x - 6
Week 3 = x
Week 4 = x + 6
Week 5 = x + 12

By doing this, you eliminate the stress of adding and then again subtracting numbers from the total.

Amount saved over 5 weeks = x - 12 + x - 6 + x + x + 6 + x + 12 (you eliminate numbers here itself)
Total = 5x
Total in dollars = 100

Therefore, x = 20.

Week 1 = x - 12 = 8.

Option B.
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Re: Samantha saved $100 in 5 weeks. Each week she saved $6 more than the [#permalink] New post   24 Mar 2022, 07:25
Explanation:

let Samantha saved x $ in the first week.
so in the coming weeks, she will save, x+6, x+12, x+18, x+24.

5 week total saving = 100
x + x+6 + x+1 + x+18 + x+24 = 100
5x + 60 = 100
x = 40/5
x = 8$

IMO-B
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Re: Samantha saved $100 in 5 weeks. Each week she saved $6 more than the [#permalink] New post   07 Apr 2023, 07:26
Expert Reply
Bunuel wrote:
Samantha saved $100 in 5 weeks. Each week she saved $6 more than the previous week. How much did she save in the first week?

A. $4
B. $8
C. $12
D. $16
E. $20


We can let the amount of money Samantha saved in the first week = n, and create the equation:

n + n + 6 + n + 12 + n + 18 + n + 24 = 100

5n + 60 = 100

5n = 40

n = 8

Answer: B
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Re: Samantha saved $100 in 5 weeks. Each week she saved $6 more than the [#permalink] New post   07 Apr 2023, 07:32
Expert Reply
Bunuel wrote:
Samantha saved $100 in 5 weeks. Each week she saved $6 more than the previous week. How much did she save in the first week?

A. $4
B. $8
C. $12
D. $16
E. $20


If your instinct is to set up an algebraic equation and introduce a variable that isn't mentioned in the question, there's a great chance you can get to the right answer easily and quickly by Plugging In The Answers (PITA). I like trying B or D.

B: 8+14+20+26+32 = $100
Done; yay!

Answer choice B.


ThatDudeKnowsPITA
ThatDudeKnowsPluggingInTheAnswers
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Re: Samantha saved $100 in 5 weeks. Each week she saved $6 more than the [#permalink]
07 Apr 2023, 07:32
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