Question

Divide 75 into two parts so that twice the greater equals three times the smaller

Answer 1

g = the greater part

s = the smaller part


2 g = 3 s Divide both sides by 2

g = ( 3 / 2 ) s


g + s = 75

( 3 / 2 ) s + s = 75

( 3 / 2 ) s + ( 2 / 2 ) s = 75

( 5 / 2 ) s = 75 Multiply both sides by 2

5 s = 75 * 2

5 s = 150 Divide both sides by 5

s = 150 / 5

s = 30


g = ( 3 / 2 ) s

g = ( 3 / 2 ) * 30 = 3 * 30 / 2 = 90 / 2 = 45


the greater part = 45

the smaller part = 30


Proof:

Twice the greater equals three times the smaller.

2 * 45 = 3 * 30

90 = 90