## Sasha and Whitney both plan to run for a spot on the school board in their city. They must each collect a certain number of signatures to ge

Sasha and Whitney both plan to run for a spot on the school board in their city. They must each collect a certain number of signatures to get their name on the ballot. So far, Sasha has 45 signatures, but Whitney just started and doesn’t have any yet. Sasha is collecting signatures at an average rate of 10 per hour, while Whitney can get 19 signatures every hour. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures.

How many hours will have gone by? How many signatures will they both have?

In ___________hours, Sasha and Whitney will each have collected _________________

## Answers ( No )

For the first question,

In five hours, Sasha and Whitney will each have collected $95.

45 + 10(y) = x ; 0+ 19(y) = x

(the equation)

10y+45=x;19y=x

Step: Solve10y+45=xfor x:

10y+45+−x=x+−x(Add -x to both sides)

−x+10y+45=0

−x+10y+45+−45=0+−45(Add -45 to both sides)

−x+10y=−45

−x+10y+−10y=−45+−10y(Add -10y to both sides)

−x=−10y−45

−x

−1

=

−10y−45

−1

(Divide both sides by -1)

x=10y+45

Step: Substitute10y+45forxin19y=x:

19y=x

19y=10y+45

19y+−10y=10y+45+−10y(Add -10y to both sides)

9y=45

9y

9

=

45

9

(Divide both sides by 9)

y=5