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.

Asked on by theta123

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jdweimer's profile pic

jdweimer | Middle School Teacher | (Level 2) Adjunct Educator

Posted on

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.

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

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.

nisarg's profile pic

nisarg | Student, Grade 11 | (Level 1) Valedictorian

Posted on

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

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

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.

ayl0124's profile pic

ayl0124 | Student, Grade 12 | (Level 1) Valedictorian

Posted on

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`

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