the sum of two numbers is 96.

Question

The sum of two numbers is 96. The difference of the two numbers is 54. What are the two numbers.

Let x be the larger number and y be the smaller number.

Write an equation that expresses the information in the sentence "The sum of two numbers is 96."   

Write an equation that expresses the information in the sentence "The difference of the two numbers is 54."   

Solve the system you have written above.

The larger number, x is . The smaller number, y is

Answer 1

Hi Ang,

We have two key pieces of information provided. Let us start by finding an equation with two variables adding to 96.

x + y = 96

The second equation to find the difference between the two variables is 54.

x - y = 54

Now format them into a system of equations:

x + y = 96

x - y = 54 <-- When doing systems of equations, pick a variable to solve for and cancel the other variable for now. We will get rid of y because it can cancel off easily. We are adding every term below:

2x = 150

x = 75

Now substitute 75 into both equations and see if y is the same solution for both.

75 + y = 96

y = 96 - 75 = 21

75 - y = 54

-y = 54 - 75

-y = -21

y = -21/-1 = 21

We see that y = 21 for both equations. We also can see that x = 75 (larger value) and y = 21 (smaller value).