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# MONEY

## Question

My goal is to have \$12. If I save \$1 a month then it will take me 12 months to save \$12. If I save \$2 a month then it will take me 6 months to save \$12. What if I saved \$1.50 each month? How many months would it take me to save \$12?

Cmon try to solve

## 5 answers to this question

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7 hours ago, ThunderCloud said:

Hmmm, I'll go for the seemingly obvious…

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8 ?

Spoiler

I tend to agree with 8. If the problem is exponential and not linear, how come "9" is right in the middle between 6 and 12? After all, 12*1 = 12, 6*2 = 6, and 8*1.5 = 12, whereas 9*1.5 = 13.5!

Spoiler

Sorry ... nobody said 9! Didn't read carefully!!!

10 minutes ago, rocdocmac said:
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I tend to agree with 8. If the problem is exponential and not linear, how come "9" is right in the middle between 6 and 12? After all, 12*1 = 12, 6*2 = 6, and 8*1.5 = 12, whereas 9*1.5 = 13.5!

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The trick answer's 9 months. Because if 1 dollar is 12 months, and 2 dollars is six months, then 1.50 is in the middle of those two, so surely the time also has to be in the middle of the time span. The number in the middle of 12 and 6 is 9, so 9 months.

However, what's important to note is that this problem isn't linear but exponential. That is, the change in time spent saving is much greater when we go from \$1 to \$2 than it is when we go from \$6 to \$7. So originally from \$1 to \$2, we double our initial savings amount, so we halve the time it takes. From \$1 to \$1.50, though, we increase our savings amount by 50%, so the total time it'll take is 12/(1.5)=8 months.

Of course, the simple way to do it is just to divide 12 dollars by 1.5 dollars a month, but the above answer gives a little more reasoning to it.

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Hmmm, I'll go for the seemingly obvious…

Spoiler

8 ?

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2 hours ago, flamebirde said:
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The trick answer's 9 months. Because if 1 dollar is 12 months, and 2 dollars is six months, then 1.50 is in the middle of those two, so surely the time also has to be in the middle of the time span. The number in the middle of 12 and 6 is 9, so 9 months.

However, what's important to note is that this problem isn't linear but exponential. That is, the change in time spent saving is much greater when we go from \$1 to \$2 than it is when we go from \$6 to \$7. So originally from \$1 to \$2, we double our initial savings amount, so we halve the time it takes. From \$1 to \$1.50, though, we increase our savings amount by 50%, so the total time it'll take is 12/(1.5)=8 months.

Of course, the simple way to do it is just to divide 12 dollars by 1.5 dollars a month, but the above answer gives a little more reasoning to it.

Clever. ^^; Nice explanation!

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14 hours ago, ThunderCloud said:

Hmmm, I'll go for the seemingly obvious…

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8 ?

NIIICE

13 hours ago, flamebirde said:
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The trick answer's 9 months. Because if 1 dollar is 12 months, and 2 dollars is six months, then 1.50 is in the middle of those two, so surely the time also has to be in the middle of the time span. The number in the middle of 12 and 6 is 9, so 9 months.

However, what's important to note is that this problem isn't linear but exponential. That is, the change in time spent saving is much greater when we go from \$1 to \$2 than it is when we go from \$6 to \$7. So originally from \$1 to \$2, we double our initial savings amount, so we halve the time it takes. From \$1 to \$1.50, though, we increase our savings amount by 50%, so the total time it'll take is 12/(1.5)=8 months.

Of course, the simple way to do it is just to divide 12 dollars by 1.5 dollars a month, but the above answer gives a little more reasoning to it.

Oops that's 8

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