# The sum of two numbers is 19. The sum of twice the smaller number and thrice the larger number is 48. What are the two numbers?

2
by elishaamon

Log in to add a comment

by elishaamon

Log in to add a comment

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Let x be the smaller number and be the larger number. Then,

x + y = 19

2x + 3y = 48

First equation can be transformed as x = 19 - y.

Substituting this value to the second equation, we have

2(19 - y) + 3y = 48

38 - 2y + 3y = 48

38 + y = 48

y = 48 - 38

y = 10

Substituting the value of y to either of the two equations, we have

x + y = 19

x + 10 = 19

x = 19 - 10

x = 9

The two numbers are 9 and 10.

**- D.E.**

x + y = 19

2x + 3y = 48

First equation can be transformed as x = 19 - y.

Substituting this value to the second equation, we have

2(19 - y) + 3y = 48

38 - 2y + 3y = 48

38 + y = 48

y = 48 - 38

y = 10

Substituting the value of y to either of the two equations, we have

x + y = 19

x + 10 = 19

x = 19 - 10

x = 9

The two numbers are 9 and 10.

Let y be the second number. It is the larger number.

x + y = 19

2x + 3y = 48

Using Gaussian Elimination Method:

So therefore, the numbers are 9 and 10.

Check:

9 + 10 = 19

2(9) + 3(10) = 48

18 + 30 = 48

48 = 48