Question

Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers

Answer 1

The larger number is 12 and the smaller number is 9

Explanation:

Let us first deal with the first sentence of this word problem.

Let's call the larger number L

and the smaller number S .

We know from the first sentence:

3 L = 4 S

We know from the second sentence:

L+S = 21

Let's solve this second equation for

L- L+S = 21 - L

S = 21 - L

Now we can substitute 21 - L for S in the first equation and solve for L :

3L = 4 (21 - L)

3L + 4L = 84 - 4L + 4L

7L = 84

7L/7 = 84/7

L = 12

Next we can substitute 12 for L in the solution to the second equation:

s = 21 - 12

s = 9