Question

Daylyn gets in donations and has pledges for $ 0.50 per correct answer . Brennan gets $100 in donations and has pledges for $0.25 per correct answer . Write and solve an equation that would show how many answers each of the boys would need to get correct to raise the same amount of money.

Answer 1

Let:

x = Number of correct answers

For Daylyn:

`\begin{gathered} y=80+0.5x \\ \end{gathered}`

For Brennan:

`y=100+0.25x`

how many answers each of the boys would need to get correct to raise the same amount of money? in another words:

`80+0.5x=100+0.25x`

Solve for x:

`\begin{gathered} \text{Subtract 80 from both sides:} \\ 80+0.5x-80=100+0.25x-80 \\ 0.5x=20+0.25x \\ \text{subtract 0.25x from both sides:} \\ 0.5x-0.25x=20 \\ 0.25x=20 \\ \text{divide both sides by 0.25}\colon \\ (0.25x)/(0.25)=(20)/(0.25) \\ x=80 \end{gathered}`