# Tom had a deal with his mother. She set aside $100 for him and he was told that every year he secured an A in all subjects the amount would be increased by 25%. But if he got a D in any year, the...

Tom had a deal with his mother. She set aside $100 for him and he was told that every year he secured an A in all subjects the amount would be increased by 25%. But if he got a D in any year, the amount would be reduced by 33%. Ten years later what is the amount that Tom has to get if got only A in all years except 2 in which he got a D.

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In order to find out how much money Tom would get we need to see how the amount of money would change for each grade.

An increase of 25% is the same as 100%+25%, which is 125%.

A decrease of 33% is the same as 100%-33%, which is 67%.

If Tom got an A the first year, he would have 125% of $100, or`1.25*$100=$125`

If Tom go a D the first year, he would get have 67% of $100, or

`.67*$100=$67 `

So that we can see how any amount will change, we will let the amount of money we start with be equal to `x ` .

Therefore, for every year we get an A, we will multiply the amount of money we have by `1.25 ` and for every year we get a D, we will multiply the amount of money we have by `.67 ` .

Lets say that Tom got A's for the first 8 years, and the 2 D's the last two years.

This would make the amount he got equal to:

Total=`1.25*1.25*1.25*1.25*1.25*1.25*1.25*1.25*.67*.67*x `

or

Total=` 1.25^8*.67^2*x `

Total`~~5.9605*.4489*x`

As you can see it would not matter which years you got an A or a D (commutative property).

Therefore he would get approximately:

`5.9605*0.4489*$100~~$267.57`

Tom would receive about $267.57 after his ten years.

Tom's mother had set aside $100 for him. If he was able to secure an A in all subjects in any year, the amount was to be increased by 25%. But if he got a D in any year, the amount was reduced by 33%. In 10 years, Tom was able to get all A's in 8 of years and got a D in only 2 years. The amount due to Tom after 10 years has to be determined.

When Tom was able to get all A's, the amount kept aside for him was increased by 25% and became 1 + 0.25 = 1.25 times the original amount. When he got a D, there was a 33% decrease in the amount and it became 1 - 0.33 = 0.67 times the original amount.

The original amount of $100 was increased to 1.25 times for 8 years and decreased to 0.67 times for 2 years. The final amount due after 10 years is 100*1.25^8*0.67^2 = 267.56

**According to their deal, after 10 years Tom's mother has to give him $267.56**

Tom had a deal with his mother. She set aside **$100** for him and he was told that every year he secured an** ****A in all subjects the**** ****amount would be increased**** ****by 25%**. But if he got a **D in any year, the**** ****amount would be reduced by 33%**. **Ten years later** what is the amount that Tom has to get if got only **A in all years except 2 in which he got a D.**

Amount=$100

year 1=25% = 100*25%= 100+25= 125

2=25% = 125*25%= 125+31.25= 156.25

3=25% = 156.25*25%= 156.25+39.06= 195.31

4=25% = 195.31*25%= 195.31+48.83= 244.14

5=25% = 244.14*25%= 244.12+61.04= 305.15

6=25% = 305.15*25%= 305.15+76.38= 381.53

7=25% = 381.53*25%= 381.53+95.38= 476.91

8=25% = 476.91*25%= 476.91+119.23=596.14

9= -33%=596.14*33%= 596.14-196.73=399.41

10= -33%=399.41*33%=399.41-131.81=**267.6**

**After 10 years the amount that Tom will receive is $267.6.**

he would get about 267.57 because 100 times 1.25 to the 8th power times .67 squared would get 267.57

$100x1.25^8x0.67^2= approx. $267.57.

You can use the formula for cumulative interest.

I have attached a link below.

Tom starts with 100 dollars which will increase 25% for all As each year and decrease by 33% if he receives a D. Ten years have passed and two years her got a D. The means that his total will be decreased by 33% (.33) twice. However, he got As all the other years which means his 100 dollars increased by 25% (.25) 8 times. This can be represented by the equation `100*(1.25^(8))*(.67^(2))`. You represent the 25% with 1.25 because you are increasing (100+25) and you represent the 33% by .67 because you took 33% from 100% (100-33). Your final answer should be **$267.57**.

Think of percents as decimals. 25% is equivalent to 0.25, while 33% is equivalent to 0.33. However, an increase of 25% can be seen as 1.25 (100% + 25%), while a decrease in 33% can be seen as 0.67 (100% - 33%).

Tom had gotten eight years with all As and two years with Ds.

With percentages, always make sure to multiply:

`$100 xx (1.25^8) xx (0.67^2) = $267.57`