The sum of two numbers is 17. Three times one number increased by 5 is the same as twice the other number decreased by 4. What is the larger of the two numbers?

Answer 1

So this can be solved using systems of equations. 

Let's break it down...

"The sum of two numbers is 17" <- that's our first equation. Sum means we're going to add. "two numbers" - well, we don't know what they are, so we can use x and y. (Note: x and y are just placeholders. You can use ANY placeholder as long as you keep it consistent with the second equations. x and y just mean "some number". We're going to work to find those numbers)

So for our first equation, we have two numbers being added together. So we can just write that as:

x+ y = 17

For the second equation:

"Three times one number increased by 5 is the same as twice the other number decreased by 4"

We have to work to process what is being asked. “Three times one number increased by 5”. So we know we are multiplying 3 to one of our numbers and increasing it (adding it) by 5.

So this part can be written as 3x+5

“Is the same as” just means “equal to” 

“Twice the other number decreased by 4”. So twice, means two times and “decreased by four” just tells us to subtract four.  So this part can be written as:

2y-4

Now we need to put this second equation together.

3x+5=2y-4.

So now we have our two equations:

x+y = 17

3x+5 = 2y-4

We have a few ways of solving this. We can use substitution, elimination, or graphing. I’m going to use substitution for this one.

So for substitution, we need to take one of two equations and solve for a single variable. So I’m going to take our first equation and solve for y.

x+y=17

-x.   -x

y= -x+17

Now I’m going to put “-x+17” in for the “y” in the second equations.

3x+5=2y-4

3x+5 = 2 (-x+17) - 4.  (Now distribute)

3x+5 = -2x + 34 - 4. (Now simplify)

3x+5 = - 2x + 30. (Now we need to get the x to one side)

+2x +2x

5x+5=30

 -5.  -5

5x = 25

X = 5

Now we can take the first equation and put 5 in for x to solve for y

x+y = 17

5 + y = 17

-5    -5

y= -12

So our x is 5 and our y is 12.