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