Can someone with a good mathematical background please help (Show your work and explain every step!)?

Question

Please show your work and explain each step thank you in advance! :)

1) Jackie purchased a new car in 1990. Three years later she sold it to a dealer for 40 percent less than she paid for it in 1990. The dealer then added 20 percent onto the price he paid and resold it to another customer. The price the final customer paid for the car was what percent of the original price Jackie paid in 1990? Then after explaining your answer explain why the answer is not 80.

2) In a class of 27 students, the average (arithmetic mean) score of the boys on the final exam was 83. If the average score of the 15 girls in the class was 92, what was the average of the whole class? Then after explaining your answer explain why the answer is not 87.5.

Answer 1

let x be original price of the car.



She sold it to the dealer for 0.60x (100%-40%)x



Dealer sold the car for 1.2*0.6x



Therefore the final customer paid 0.72x



or 72 percent of the original price.







Its not 80 percent because first of all you subtract the transactions. All you do is find the percent of the original its sold for and multiply it by the original.

Since all transactions were priced a proportion to the previous you just multiply the proportions.

``she sold it to a dealer for 40 percent less than she paid for it in..``

This means she sold it for 60% of original price. (100 percent - 60 percent)



2. Given: 15 girl

therefore there are 12 girls

because total has to be 27 students.



12 boys * boys` average + 15 girls * girls` average

= (12* 83) + (15*92) divide by 27(total students)

=88 %



87.5 is obtained by adding up the boys` and girls` average and dividing by 2



You can`t do this because there are more girls, and so girls have more of a weight on the class average than boys do.

If there were an equal amount of boys as girls and their respective averages didn`t change then the class average would be 87.5

Answer 2

1) x=a car value.



Jackie sold: 0.60x



Dealer resold: (1.20)(0.60x)



then final customer paid: 0.72x



Final customer paid: 72 % of the original price



The answer is not 80% because we should not add 20% of original price, but we must add 20% of the resold price.



2) boys=27-15=12

girls=15



The average of the whole class is

[(12)(83)+(92)(15)]/27=88



The answer is not 87.5 because this average would consider that the number of boys and girls is the same and it is not correct.



You have a nice day

Zogu50



PD: Excuse my bad spelling but I'm Peruvian

Answer 3

1. give the car a value.

1000

sold it for 600

turned around and sold it for 720



720=x*1000

.72 or 72%



2. (12*83)+(92*15)/27

=88