Question

In an election for senior class president, Alice received 30 votes more than David. If the ratio of the number of votes Alice received to the number of votes David received was 8 to 7, how many votes did David receive?

a. 30
b. 49
c. 64
d. 210
e. 240

Answer 1

You'll have 1 equation, so let x = votes Aliced received and y = voted David recieved
\[\frac{ x }{ y } = \frac{ 8 }{ 7 }\]

Answer 2

Let David's votes be d votes. Then Alice's votes = d + 30. So we can write this equation:
\[\large \frac{d+30}{d}=\frac{8}{7}\]
Now just solve for d.

Answer 3

That works nicely to I believe, and 2 equations* letting x = y + 30

Answer 4

Quite right :)

Answer 5

7(d + 30) = 8d
7d + 210 = 8d
210 = d

oh lol. easier than i thought :) thank you. i thought i would have to make the proportion 8/15, not 8/7

Answer 6

You're welcome :)