Question

One third the sum of two numbers is 10 and half the difference is 14. What is the larger number?

Answer 1

a = larger number

b = smaller number

One third the sum of two numbers is 10.

This mean:

( a + b ) / 3 = 10 Multiply both sides by 3

a + b = 30

Half the difference is 14.

This mean:

( a - b ) / 2 = 14 Multiply both sides by 2

a - b = 28 Add b to both sides

a - b + b = 28 + b

a = 28 + b

Replace this value in equation:

a + b = 30

( 28 + b ) + b = 30

28 + 2 b = 30 Subtract 28 to both sides

28 + 2 b - 28 = 30 - 28

2 b = 2 Divide both sides by 2

b = 1

a = 28 + b = 28 + 1 = 29


The larger number = 29


Proof :

( a + b ) / 3 = ( 29 + 1 ) / 3 = 30 / 3 = 10


( a - b ) / 2 = ( 29 - 1 ) / 2 = 28 / 2 = 14