Question

Irma and Maggie 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, Irma has 45 signatures, but Maggie just started and doesn't have any yet. Irma is collecting signatures at an average rate of 6 per hour, while Maggie can get IS 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 signatures will they both have? How many hours will have gone by? Answer using graphing, substitution, and elimination methods.

Answer 1

Irma and Maggie will both have 36/IS signatures. It will take them 6/IS hours to collect the same number of signatures.

Let's start by setting up an equation to represent the situation. Let x represent the number of hours it takes for Maggie to collect the same number of signatures as Irma. Since Irma is collecting signatures at a rate of 6 per hour, the number of signatures she will have after x hours is 6x. Maggie, on the other hand, is collecting IS signatures every hour, so the number of signatures she will have after x hours is ISx.

We want to find the value of x when the number of signatures collected by both Irma and Maggie is the same. This can be represented by the equation 6x = ISx. To solve for x, we can divide both sides of the equation by IS: x = 6/IS.

Now, to find the number of signatures they will both have, we can substitute the value of x back into either equation. Using the equation 6x, we have 6 * (6/IS) = 36/IS signatures.

So, they will both have 36/IS signatures, and it will take them 6/IS hours to collect the same number of signatures.