The difference of two numbers is 8. The sum of 2 times the larger number plus 3 times the smaller number is 146.

Answer 1

let's call our numbers A and B. Let's say B is the larger number.

we know the difference is 8. What does difference mean? It means we are subtracting.

so, B - A = 8

what does sum indicate? addition.

"two times the larger number" = 2 x B

"three times the smaller number" = 3 x A

is 146 generally means equals so, =146

So, when we piece it together we get:

B - A = 8

2B + 3A = 146

let's solve for one of the variables, so we can have our bigger equation all in the same terms

B - A = 8

subtract A from both sides

B = 8 + A

Now plug that in wherever you see B in the larger equation

2B + 3A = 146

2(8 + A) + 3A = 146

distribute

16 + 2A + 3A = 146

combine like terms

16 + 5A = 146

solve for A

5A = 140

A = 28

now use A to solve for B

B - A = 8

B = 8 + A

A = 28

B = 8 + 28

B = 36

Ao, the larger number is 36 and the smaller number is 28