What’s the larger number?

Question

The sum of two numbers is 79. If twice the smaller number is added to the larger number, the result is 112. Find the larger number.

Answer 1

Hi Trevor,

To solve this problem, we can create 2 equations with 2 unknowns and solve the system of equations using elimination.

Let's use the variable, x , to represent the smaller of the two numbers and the variable, y , to represent the larger of the two numbers.

Since their sum is 79, we can write our first equation as:

x + y = 79

Then we can write the following equation to show that "twice the smaller added to the larger is 112" :

2x + y = 112

Now we can use elimination to solve these two equations. Let's multiply the first equation by -1 to do so:

x + y = 79 becomes -x - y = -79

2x + y = 112

Then:

-x - y = -79

2x + y = 112

x = 33

The smaller number will be 33

The larger number will be 46 because 79 - 33= 46