Question

The sum of two numbers is 101/10 and one is 9/10 of the other. Find the numbers. Please solve it step by step without using “x or a factor”.

Answer 1

Let the two numbers is x, y.

The sum of two numbers is x+ y = 101/10 ------------>(1)

And one is x = 9/10

Substitute x = 9/10 in the equation (1)

9/10 + y = 101/10

Subtract 9/10 from each side.

y = 101/10 - 9/10

Rewrite the expression with common denominator.

y = [101 - 9] / 10

y = 92/10

Therefore x = 9/10 and y = 92/10.

Check: x + y = 9/10 + 92/10

x + y = (9 + 92)/10 = 101/10.

Answer 2

Let the two numbers is x, y.

The sum of two numbers is x+ y = 101/10 ------------>(1)

And one is x = (9/10)y

Substitute x = (9/10)y in the equation (1)

(9/10)y + y = 101/10

Rewrite the expression with common denominator.

(9y + 10y)/10 = 101/10

Multiply each side by 10.

19y = 101

Divide each side by 19.

y = 101/19

Substitute y = 101/19 in the x = (9/10)y

x = (9/10)(101/19) = 909/190

Therefore x = 909/190 and y = 101/19

Check: x + y = 909/190 + 101/19

Rewrite the expression with common denominator.

x + y = (909 + 1010)/190 = 1919/190 = 101/10.