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

The larger number is 12 and the smaller number is 9

Step-by-step 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

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step-by-step explanation: