Thread: Cars Sold During First Quarter

1. Cars Sold During First Quarter

During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24 percent greater than the number sold during the first quarter of 1984, how many were sold during the first quarter?

My effort is shown below.

Let c = number of cars sold during the first quarter in 1984

0.24c = 2,976,000

Solving for c, I got 12,400,000 cars.

I then subtracted 2,976,000 from c.

My answer is 9,424,000 cars sold during the first quarter in 1984. The book's answer is 2,400,000 cars.

2. Re: Cars Sold During First Quarter

You want:

1.24c = 2,976,000

3. Re: Cars Sold During First Quarter

Originally Posted by harpazo
During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24 percent greater than the number sold during the first quarter of 1984, how many were sold during the first quarter?
Let c = number of cars sold during the first quarter in 1984
0.24c = 2,976,000
Solving for c, I got 12,400,000 cars.
I then subtracted 2,976,000 from c.
My answer is 9,424,000 cars sold during the first quarter in 1984. The book's answer is 2,400,000 cars.
Well, you knew answer should be LESS than 2,976,000; so why did you not try again?

Good idea to make up an easier but similar problem to see how it works; like:

During the second quarter of 1984, a total of 110 domestic cars were sold.
If this was 10 percent greater than the number sold during the first quarter of 1984,
how many were sold during the first quarter?

c + .10c = 110
1.10c = 110
c = 110 / 1.10 = 100

Now using actual:
c + .24c = 2976000
1.24c = 2976000
c = 2976000 / 1.24 = 2400000

4. Re: Cars Sold During First Quarter

Yes the problem is essentially asking you to find a number, such that when it is increased by 24%, the result is 2,976,000.

5. Re: Cars Sold During First Quarter

Originally Posted by harpazo
During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24 percent greater than the number sold during the first quarter of 1984, how many were sold during the first quarter? My effort is shown below.
Let c = number of cars sold during the first quarter in 1984. The book's answer is 2,400,000 cars.
To harpazo, I have given you the form twice before.
$\dfrac{\text{new }-\text{ old }}{\text{ old }}=\%$ of change.

Solve $\dfrac{2976K-x}{x}=0.24$ SEE HERE.

6. Re: Cars Sold During First Quarter

Originally Posted by harpazo
During the second quarter of 1984, a total of 2,976,000 domestic cars were sold. If this was 24 percent greater than the number sold during the first quarter of 1984, how many were sold during the first quarter?

My effort is shown below.

Let c = number of cars sold during the first quarter in 1984

0.24c = 2,976,000

Solving for c, I got 12,400,000 cars.

I then subtracted 2,976,000 from c.

My answer is 9,424,000 cars sold during the first quarter in 1984. The book's answer is 2,400,000 cars.
Always check the reasonableness of your answer by taking it back to the question.

If 2,976,000 is greater than the first quarter's sales then you should expect your answer to be less than 2,976,000. Your answer can't possibly be correct, so you need to rethink the problem.

7. Re: Cars Sold During First Quarter

Originally Posted by MarkFL
You want:

1.24c = 2,976,000
Where did 1.24 come from?

8. Re: Cars Sold During First Quarter

Originally Posted by MarkFL
Yes the problem is essentially asking you to find a number, such that when it is increased by 24%, the result is 2,976,000.
What about x + 0.24x = 2,976,000?

9. Re: Cars Sold During First Quarter

Originally Posted by harpazo
What about x + 0.24x = 2,976,000?
Yes, that would be correct, and then:

$\displaystyle x(1+0.24)=2976000$

$\displaystyle 1.24x=2976000$

Which shows you where the 1.24 comes from.

10. Re: Cars Sold During First Quarter

Thank you everyone. Good study notes here.