the sum of two numbers is 34. the larger number is 10 more than the smaller number. what are the numbers?

Question

I couldnt get it on my own

Answer 1

Hi Ariel!

Let's try taking these sentences and translating them into an expression or an equation if we can.

"The sum of two numbers is 34". We know we have two distinct, unknown numbers, so let's just call them x and y. We know the sum of the numbers is 34. As an equation, this is expressed as x + y = 34.

The second part says "The larger number is 10 more than the smaller number". Let's just call x the larger number and y the smaller number. As an equation, this is written as x = y + 10.

This is a system of equations! There are two equations and two unknown quantities. There are different ways to solve a system of equations, but the easiest one to use in this case is known as substitution. During substitution, you take one equation and solve it for one variable. Then, take that new expression and plug it into the other equation... in words it might be hard to follow so let's look at it with our equations.

x + y = 34

x = y + 10

During substitution, you pick one equation and solve it for one of the variables (aka isolate one of the variables). Fortunately, the second equation is already solved for x!

Now, substitute the second expression in for "x" in the first one.

y + 10 + y = 34

Now you can solve for y.

2y + 10 = 34

2y = 24

y = 12.

If y is 12, you know that x has to be 22, since 12 + 22 is 34.

Hope this helped! :)