Mathematics 41 Online OpenStudy (anonymous):

the sum of two numbers is 31. The first is 5 less than the second. Find the numbers. OpenStudy (shadowfiend):

Can you convert this into an equation? OpenStudy (anonymous):

x=5-y ?? OpenStudy (shadowfiend):

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

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 OpenStudy (shadowfiend):

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

Can you solve that system of equations? OpenStudy (anonymous):

y-5+y OpenStudy (anonymous):

=31 OpenStudy (shadowfiend):

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? OpenStudy (shadowfiend):

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? OpenStudy (shadowfiend):

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? OpenStudy (shadowfiend):

Exactly. OpenStudy (anonymous):

thats where i went wrong. y=18? OpenStudy (shadowfiend):

Exactly. OpenStudy (shadowfiend):

And then what's x? OpenStudy (anonymous):

x=18-5=13 OpenStudy (anonymous):

13 OpenStudy (shadowfiend):

Exactly! OpenStudy (anonymous):

thank you. i am going to attempt my next problem. OpenStudy (shadowfiend):

Cool.

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