# Math Help - Find Larger Number

1. ## Find Larger Number

The difference between 2 positive numbers is 9. If 4 times the larger number is 10 times the smaller, what is the larger number?

Let L = larger number

Let S = smaller number

My equations:

L - S = 9
4L = 10S

After doing the math, I came up with the larger number being 90.

According to the math book, my answer is wrong.

What did I do wrong?

Are the equations wrong?

2. ## try again

FYI, I'm not your personal tutor, lol.

Ok, so if you isolated S and substituted, then you should've gotten $4L = 10 \times (L - 9)$

see what happens with it from there.

3. Originally Posted by magentarita
The difference between 2 positive numbers is 9. If 4 times the larger number is 10 times the smaller, what is the larger number?

Let L = larger number

Let S = smaller number

My equations:

L - S = 9
4L = 10S

After doing the math, I came up with the larger number being 90.

According to the math book, my answer is wrong.

What did I do wrong?
Since you didn't show your steps in solving, there's no way to know where you might have "done wrong". Sorry!

Thank you for showing your set-up. Your equations look fine to me. To solve, let's try substitution:

. . . . .L - S = 9

. . . . .L = S + 9

. . . . .4(S + 9) = 10S

. . . . .4S + 36 = 10S

. . . . .36 = 6S

. . . . .6 = S

Then what must L equal?

Note that you can check your answer to any "solving" problem by plugging it back into the original exercise. If the larger number were, as you propose, equal to 90, then the smaller number will be 90 - S = 6, or S = 84. But 4(90) = 360, and 10(84) = 840.

4. ## Then L =

Originally Posted by stapel
Since you didn't show your steps in solving, there's no way to know where you might have "done wrong". Sorry!

Thank you for showing your set-up. Your equations look fine to me. To solve, let's try substitution:

. . . . .L - S = 9

. . . . .L = S + 9

. . . . .4(S + 9) = 10S

. . . . .4S + 36 = 10S

. . . . .36 = 6S

. . . . .6 = S

Then what must L equal?

Note that you can check your answer to any "solving" problem by plugging it back into the original exercise. If the larger number were, as you propose, equal to 90, then the smaller number will be 90 - S = 6, or S = 84. But 4(90) = 360, and 10(84) = 840.

.L - 6 = 9...Then L = 9 + 6 or 15