The sum of two numbers is 70.one number is 4 times as large as the other.What are the numbers?

Question

It’s an systems of equations problem

Answer 1

We have 2 unknowns, so we must have 2 equations to solve this.

Let x=smaller number

     y=larger number

Eq. I:    x+y=70

Eq. II:   y=4x

Using the substitution method, we can use the value of y from Eq. II in terms of x in Eq. II and then solve for x.

            x+y=70            Eq. I

            x+4x=70          substitute value of y from Eq. II

            5x=70              simplify

            x=70/5             divide both sides by 5 to isolate x on one side

            x=14                solve for x

Use this value for x in Eq. I and solve for y.

            x+y=70            Eq. I

            14+y=70          substitute for 14 for x

            y=70-14           subtract 14 from both sides

            y=56                solve for y

The 2 numbers are 14 & 56.