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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Brenda and Eduardo 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, Brenda has signatures, and Eduardo has . Brenda is collecting signatures at an average rate of per day, whereas Eduardo is averaging 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?In days, Brenda and Eduardo will each have collected signatures.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Brenda and Eduardo 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, Brenda has signatures, and Eduardo has . Brenda is collecting signatures at an average rate of per day, whereas Eduardo is averaging 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?In days, Brenda and Eduardo will each have collected signatures.
- Define Variables: Let's define the variables.Let be the number of days after which Brenda and Eduardo will have the same number of signatures.Let be the number of signatures they will each have at that point.
- Write Equations: Write the equations based on the given information.Brenda starts with signatures and collects per day. So after days, she will have signatures.Eduardo starts with signatures and collects per day. So after days, he will have signatures.They will have the same number of signatures when .
- Solve Equation for x: Solve the equation for x.Subtract from both sides:
- Calculate Number of Signatures: Calculate the number of signatures they will each have after days.Since , we substitute into Brenda's signature count equation:
- Verify Result: Verify the result by checking Eduardo's signature count.Both Brenda and Eduardo will have signatures after days, which confirms our solution is correct.
