Ashley P. answered • 02/19/21

A high-achieving college freshman with a 1500 SAT score

Hi Grace!

Word based problems can be confusing, but once you get used to a few familiar words and phrases it should help you out. So, there are two numbers, x (larger) and y (smaller).

The sum of the two numbers equals 26. This means that when x is added to y, you get 26.

Your first equation is x+y=26

The next equation sounds a little more difficult. Let's break it down:

the difference between three times the larger and twice the smaller is 18.

We can gain a few bits of knowledge from this:

- we will be subtracting
- The larger number, x, has a coefficient of 3
- The smaller number, y, has a coefficient of 2
- We will be subtracting in the form x-y. This is due to the order of the mentioned variables

From there, we can write the equation:

3x-2y=18

And now we have our 2 equations:

x+y=26

3x-2y=18

To solve, let's use substitution. Because there is an equation with variables that don't have coefficients, it will be the easier to work with.

x+y=26

Now, solve for y or x

x=26-y

Plug the value of x into the equation:

3(26-y)-2y=18

78-3y-2y=18

78-5y=18

Now, combine terms so that you can solve for y

5y=60

y=12

Now, we can plug the new value of y into either equation (I will plug it into the first, but it's always good to plug it into both and solve for x)

x+12=26

x=14

your answers are x=14 and y=12

Grace F.

Thank you so much. This is one of the most thorough and easy to understand answers i've ever gotten.02/19/21