the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343. find the numbers.

Answer is x = 68 and y = 55

Let’s assume the two numbers are x and y

X + y = 123 — (1)

X + 5y = 343 — (2)

Write (1) in terms of x

X = 123 - y — (3)

Use in (2)

123 - y + 5y = 343

Rearrange to have only y terms on the right.

-y +5y = 343 - 123

4y = 220

y = 220/4 = 55

Found y = 55

Use y = 55 in (3)

X = 123 - 55 = 68

Found x = 68