Mathematics 60 Online
OpenStudy (anonymous):

the sum of two numbers is 31. The first is 5 less than the second. Find the numbers.

Can you convert this into an equation?

OpenStudy (anonymous):

x=5-y ??

Not quite, it's $$x = y - 5$$ (making $$y$$ 5 less than $$x$$).

So that's the first part, what about the part where it says that `the sum of two numbers is 31'. Can you make that into an equation?

OpenStudy (anonymous):

x+y=31

Right. So now you have two equations: \begin{align} x + y &= 31\\ y - 5 &= x \end{align}

Can you solve that system of equations?

OpenStudy (anonymous):

y-5+y

OpenStudy (anonymous):

=31

Right, and then can you solve that equation for y?

OpenStudy (anonymous):

that is where i am a little confused. do i minus a y?

OpenStudy (anonymous):

4y?

So you have: y - 5 + y = 31 You can put the ys together: y + y - 5 = 31 Which is the same as: 2y - 5 = 31

OpenStudy (anonymous):

2y=26?

Not quite, remember that if we want to move the 5 over to the right, you have to add 5 to both sides to cancel it on the left: 2y - 5 + 5 = 31 + 5 2y = 36

OpenStudy (anonymous):

oh so i have to add 5 to equal it out since it is negative?

Exactly.

OpenStudy (anonymous):

thats where i went wrong. y=18?

Exactly.

And then what's x?

OpenStudy (anonymous):

x=18-5=13

OpenStudy (anonymous):

13

Exactly!

OpenStudy (anonymous):

thank you. i am going to attempt my next problem.