The sum of two numbers is 64. Their difference is 14. Find each of the numbers.

Question

I just don't know what I am supposed to do in order to get the answer. The question that this lesson is off of, my teacher didn't show us how to turn the word problem into an equation. Plus every answer that I get that adds up to be 64, there difference is not 14. I just know how to look at a system of linear equations and solve them by substitution. Can someone just please show me how I am and supposed to do word problems like this one?

Answer 1

Hey Izabell! For this problem, we would start by defining the "two numbers" that they describe in the problem. We can call them whatever we want to, but I prefer to use x and y.

They say that the sum of the two numbers (x and y) is 64, so we can write our first equation by adding them and setting that sum equal to 64:

x + y = 64

The question also tells us that their difference is 14. Similarly to before, we'll just subtract the two numbers and set that difference equal to 14:

x - y = 14

Now from here, you know how to continue with substitution to find the values for x and y. Just remember when you get a word problem to break it down and look for key words like sum, difference, or product, and from there you'll be able to build your system of equations.

I hope this helped, and if you have any questions, feel free to reply or contact me!

Answer 2

x + y = 64

x - y = 14

2x = 74 Add the two equations

x = 36

y = 28