Write a system of equations to describe the situation below, solve using substitution , and fill in the blanks . Zoe and Sarah each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far , Zoe has 10 signatures , and Sarah has 12. Zoe is collecting signatures at an average rate of 10 per day, whereas Sarah is averaging 8 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How many signatures will they both have ? How long will that take? Zoe and Sarah will each have collected signatures in days.

Answer 1

Let x be the number of days it will take for Zoe and Sarah to collect the same number of signatures.

The number of signatures Zoe will have collected after x days is 10 + 10x.
The number of signatures Sarah will have collected after x days is 12 + 8x.

Setting the two expressions equal to each other:
10 + 10x = 12 + 8x

Subtracting 8x from both sides:
2x = 2

Dividing by 2:
x = 1

Therefore, it will take Zoe and Sarah 1 day to collect the same number of signatures.

Substitute x = 1 back into either equation to find the number of signatures they will both have:
10 + 10(1) = 10 + 10 = 20

So, Zoe and Sarah will each have collected 20 signatures after 1 day.