As part of their government class, Maddie and Ryan had to log volunteer hours in their community. Ryan volunteered for one more than three times the number of hours that Maddie did. Altogether, they volunteered in their community for 45 hours, how many hours did Ryan volunteer?

Step-by-step explanation:

Maddie = y

Ryan = x

One more than means to (add 1)

Three times means to (multiply by 3)

Maddie worked for y hours

Ryan worked for

* x hours

* three times the number of hours that Maddie did

x = 3y

one more than

x = 3y + 1

Altogether

x + y = 45 hours

(3y +1) + y = 45

3y + y = 45-1

4y = 44

y= 44/4

y =11

Ryan hours (x)

x = 3y + 1

x= 3(11) + 1

x =33+ 1

x=34

Maddie hours (y)

y=11

x + y= 45

34+11= 45

Ryan: 34 hours

Maddie: 11 hours

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1