One number is 4 plus half another number. Their sum is 31. Find the numbers

13 and 18.

write an equation for each statement

:

"One number is 4 plus one-half of another."

x = 1%2F2y + 4

get rid of the fraction, multiply by 2 and you have:

2x = y + 8

:

"The sum of the numbers is 31. "

x + y = 31

y = (31-x); use this for substitution

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let numbers are x and y.

according to question x+y = 31 ... (1)

and

x = y/2 + 4 ... (2)

now, from (2) x-4 = y/2

=> 2x - 8 = y

from (1) we find y = 31-x

compare both value of y ...

2x-8 = 31-x

=> 2x + x = 31+8

=> 3x = 39

=> x = 13

y = 31-13 = 18