Question

Janice and Will 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, Janice has 10 signatures, and Will has 14. Janice is collecting signatures at an average rate of 9 per day, whereas Will is averaging 5 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?

Answer 1

It will take 1 day for Janice and Will to have the same number of signatures, and they will both have 19 signatures.

Step-by-step explanation:

To find out how long it will take for Janice and Will to collect the same number of signatures, we need to set up an equation. Let x represent the number of days it takes for them to have the same number of signatures. Janice is collecting 9 signatures per day, so after x days, she will have 10 + 9x signatures. Will is collecting 5 signatures per day, so after x days, he will have 14 + 5x signatures. We can set up the equation: 10 + 9x = 14 + 5x. Now we can solve for x:

1. Subtract 5x from both sides: 10 + 4x = 14.
2. Subtract 10 from both sides: 4x = 4.
3. Divide both sides by 4: x = 1.

Therefore, it will take 1 day for Janice and Will to have the same number of signatures. To find out how many signatures they will both have, we can substitute x = 1 into one of the equations. Let's use Janice's equation: 10 + 9(1) = 10 + 9 = 19.

So, it will take 1 day for Janice and Will to have the same number of signatures, and they will both have 19 signatures.