The larger of two numbers is four times the smaller number increased by 9. If the sum of the numbers is 29, what is the smaller number?

Answer 1

Aidan,

Read my answer carefully, and then you will be able to do other problems similar to this one. The key to solving this problem is knowing how to translate English sentences into mathematical sentences. Here it goes!

The larger of two numbers is four times the smaller number increased by 9. If the sum of the numbers is 29, what is the smaller number?

We know there are two numbers. Let's call them x and y with y being the larger of the two numbers.

The first English sentence in the problem translates to:

y = 4x + 9

The second English sentence in the problem translates to:

x + y = 29

We are asked to find the smaller number, which is x.

I will use the substitution method of solving this system of two equations. I am going to substitute the value of y as shown in the first equation for y in the second equation.

y = 4x + 9

x + y = 29

x + (4x + 9) = 29

x + 4x + 9 = 29

5x + 9 = 29

5x + 9 – 9 = 29 – 9

5x = 20

x = 4

I believe that it is best to answer word problems with words, so here's the answer: The smaller of the two numbers is 4.

Answer 2

S - smaller number

L - larger number

Writing the system of equations:

L = 4S + 9

L + S = 29

Substituting 1st expression into 2nd equation:

4S + 9 + S = 29

5S = 20

S = 4