Question

'Two numbers add up to 70. One third of the larger number is 10 more than one seventh of the smaller number. Find the numbers.' - Please explain the sum clearly.

Answer 1

Let the larger number be 'x' and the smaller number be 'y'.

Given : x + y = 70

1/3* x = 10 + 1/7* y. ~(1)

x + y = 70

x = 70 - y ~(2)

substitute (2) in (1)

1/3 * ( 70 - y ) = 10 + 1/7 *y

70/3 - y/3 = 10 + y/7

y/7 + y/3 = 70/3 - 10

3y + 7y / 21 = 70 - 30 / 3

10y/ 21 = 40/3

10y = 40/3 * 21

10y = 40 * 7

10y = 280

y = 280 /10

y = 28

x = 70 - y

x = 70 - 28

x = 42