Question

I am thinking of two positive numbers in the ratio $5:3$. The difference between the two numbers is $90$. What is the sum of the two numbers?.

Answer 1

The sum of the two numbers is $ 360

Let the bigger number be x

Let the smaller number be y

From the question given above, we were told that two numbers exist in ratio $ 5 : $ 3

Thus,

x : y = 5 : 3

x/y = 5/3

Cross multiply

x = 5y/3 ............ (1)

Also, we were told from the question that difference between the two numbers is $ 90 i.e

x – y = 90 ........... (2)

Substitute the value of x in equation (1) into equation (2). We have:

x = 5y/3 ............ (1)

x – y = 90 ........... (2)

5y/3 – y = 90

Multiply through by 3

5y – 3y = 270

2y = 270

Divide both side by 2

y = 270 / 2

y = $ 135

Substitute the value of y into equation 1 to obtain the value of x.

x = 5y/3 ............ (1)

y = $ 135

x = (5 × 135)/3

x = 675 / 3

x = $ 225

Finally, we shall determine the sum of the two numbers.

• x = $ 225

• y = $ 135

• Sum =?

Sum = x + y

Sum = 225 + 135

Sum = $ 360

Thus, the sum of the two numbers is $ 360

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