Expert: Bobby Soltani - 7/18/2009

Question
The sum of two numbers is 71.  The second is 6 more than 4 times the first.  What are the two numbers?

Answer
Hi Jennifer,

These types of problems are sometimes called "two equations two unknowns" type problems.  There are several ways to solve them, but basically you want to rewrite the two sentences into two equations each having two variables, such as x and y.  Here's an example:

The sum of two numbers is 71.

x + y = 71   (equation 1)

x is one number, and y is the other.

The second (y) is (=) 6 more (+)than 4 times (multiply) the first (x).

y = 6 + 4x  (equation 2)

x + y = 71
y = 6 + 4x

There are lots of ways to solve these types of equations, including addition, substitution, using matrices, and other ways.  I will show you one example using substitution.

We know from equation 2 that y is the same as 6 + 4x, so we can substitute 6 + 4x in for y in the first equation.  That gives us

x + (6 + 4x) = 71

now we have an equation with only one variable and we can solve for x.

5x + 6 = 71

5x = 65

x = 13

Now, we can plug 13 in for x into either the first or second equation and solve for y.

Let me know if you have any questions.

Bobby