# Thread: Help with this word problem!

1. ## Help with this word problem!

The value of a new car of a particular make, A, decreases by 22.5% during the first year. In the second year, its value decreases by 12.5% of its value at the beginning of the year. The value of a new car of another make, B, decreases by 25% during the first year. In the second year, its value decreases by 15% of its value at the beginning of the year. A new car of make A costs $48,000 and a new car of make B costs$42,000.

(a) What is the difference between the values of the two cars at the end of the firts year? Express this differnce as a percentage of the value of the car of make A at the end of the first year.

(b) Calculate the difference between the values of the two cars at the end of the second year.

Thankyou!

2. Originally Posted by laser2302

The value of a new car of a particular make, A, decreases by 22.5% during the first year. In the second year, its value decreases by 12.5% of its value at the beginning of the year. The value of a new car of another make, B, decreases by 25% during the first year. In the second year, its value decreases by 15% of its value at the beginning of the year. A new car of make A costs $48,000 and a new car of make B costs$42,000.

(a) What is the difference between the values of the two cars at the end of the firts year? Express this differnce as a percentage of the value of the car of make A at the end of the first year.

(b) Calculate the difference between the values of the two cars at the end of the second year.

Thankyou!
If something decreases by 22.5% means it is worth 77.5% perfect of the original price.
In the beggining the car was worth $x$ after the first year is it $.775x$ after the second year it decreases by 12.5% meaning its value is 87.5% of the new price thus,
$.875(.775x)=.678125x$
Similarily the second car after two years is,
$.85(.75x)=.6375x$ and $.75x$ after one year.

The first problem asks for the difference after the first year.
The first car is worth $.775\times 48,000=37,200$. The second car is worth $.75\times 42,000=31,500$ The difference is,
$37,200-31,500=5,700$

After two years, you have the new values,
$.875\times 37,200=32,250$
$.85\times 31,500=26,775$
Their difference is,
$32,250-26,775= 5475$

3. Originally Posted by ThePerfectHacker
The first problem asks for the difference after the first year.
The first car is worth $.775\times 48,000=37,200$. The second car is worth $.75\times 42,000=31,500$ The difference is,
$37,200-31,500=5,700$
The question asks to write this out in terms of the percentage of the price of car A, so you divide 5,700 by the price of car A

$\frac{5700}{37200}=0.153225806\approx\boxed{15
\text
{percent}}$

4. Hello, laser2302!

Are you sure you can't work this out yourself?

[quote]The value of a new car of a particular make, $A$, decreases by 22.5% during the first year.
In the second year, its value decreases by 12.5% of its value at the beginning of the year.

The value of a new car of another make, $B$, decreases by 25% during the first year.
In the second year, its value decreases by 15% of its value at the beginning of the year.

A new car of make $A$ costs $48,000 and a new car of make $B$ costs$42,000.

(a) What is the difference between the values of the two cars at the end of the first year?
Express this differnce as a percentage of the value of the car of make A at the end of the first year.

(b) Calculate the difference between the values of the two cars at the end of the second year.

During year 1, make $A$ loses $22.5\%\text{ of }\48,000 \:=\:0.225 \times 48,000 \:=\:\10,800$
. . . At the end of year 1, it is worth only: $\48,000 - 10,800 \:= \:\37,200$

During the year 2 $A$ loses $12.5\%\text{ of }\37,200 \:=\:0.125 \times 37,200 \:= \:\4,650$
. . . At the end of year 2, it is worth only: $\37,200 - 4,650\:=\:\32,550$

During year 1, make $B$ loses $25\%\text{ of }\42,000\:=\:0.25 \times 42,000 \:=\:\10,500$
. . . At the end of year 1, it is worth only: $\42,000 - 10,500\:=\:\31,500$

During year 2, $B$ loses $15\%\text{ of }\31,500 \:=\:0.15 \times 31,500\:=\:\4,725$
. . . At the end of year 2, it is worth only: $\31,500 - 4,725\:=\:\26,775$

Now that we've worked all the numbers, we can answer the questions.

(a) The difference in value at the end of year 1 is:
. . . . . $\37,200 - 31,500\:=\:\5,700$ . . .
Boy, that was hard!

The percentage they asked for is: $\frac{5.700}{37,200}\:=\:0.153225806\:\approx\:15. 3\%$

(b) The difference in value at the end of year 2 is:
. . . . . $\32,550 - 26,775\:=\:\5,775$ . . .
I need a nap!

5. Originally Posted by Soroban
Hello, laser2302!

Are you sure you can't work this out yourself?
You know you really shouldn't be so critical, after all, people come here for reassurance and help (or, unfortunately, so they don't have to do the work) and should be treated well.