The sum of two numbers is 93. It four times a smaller number is subtracted from the larger number, the result is 13. Find the two numbers

Answer 1

Hello Ashley,

You must be in your Linear Systems Unit. This type of problem requires that you set up two separate equations.

Let's start by setting up what our two variables will be. How about this:

L = larger number

S = smaller number

Now circle the word SUM. That means to add right? So your first equation is:

L + S = 93.

Now look at the second sentence. Let's translate the phrases into "mathese".

"Four times a smaller number" 4S

"is subtracted from the larger number" So L - 4S

"the result is" (that's the verb) where you'll put =

So: L - 4S = 13 is my second equation.

So now we have the system

L + S = 93

L- 4S = 13

At this point, you could solve this linear system by elimination or by using substitution. Which of those methods do you like the best? It really doesn't matter but since I see an L in the first equation and an L in the 2nd equation, they would be very easy to make eliminate.

So I will multiply the first equation by -1 (remember to multiply EVERY TERM by -1)

Now I have:

-L - S = -93 Add the columns of like-terms

L - 4S = 13

-5S = -80 Divide both sides by -5

So S = 16.

Plug that 16 into one of the original 2 equations in place of the S (I'll use the first equation...)

-L - 16 = -93 Add 16 to both sides

-L = -77 Multiply both sides by -1

L = 77

So my smaller number is 16 and my larger number is 77. Wasn't that fun! I love systems of equations :)

Enjoy your math class this week!

Jetta McGinniss

Answer 2

n = larger number

m = smaller number

The given information translates into two equations:

n + m = 93

n - 4m = 13

Solve for n and m. From the top equation, get

n = 93 - m

Plug this in the place of n in the bottom equation, and solve for m. Then plug the result for m into either equation and solve for n. Test the answers.