Question

The sum of two numbers is 40. When the greater number is divided by the smaller, the quotient is 4 and the remainder is 5. What are the numbers?

Answer 1

num1 `(x) = 33`
num2 `(y) = 7`

Explanation:

Let num1 = x and num2 = y

We know that

eq1: `x + y = 40`

eq2: `x/y = 4 r 5`

We solve these simultaneous equations by solving for one variable, in this case, I solve for `x` by isolating `x` in eq2

`x = 4y r 5`

We substitute this value of `x` in eq1

`4yr5 + y = 40`

We simplify and solve for y

`4y + y = 35`
`5y =35`
`y = 7`

We substitute `y` into one of the original equations and solve for `x`, in this case, eq1

`x + 7 = 40`
`x = 40 - 7`
`x = 33`

`x = 33`
`y = 7`