Question

7.63. Kim was elected class president. She received 3 votes for every 2 that Amy got. No one else ran. However, if 8 of the people who voted for Kim had voted for Amy instead, Kim would have received only 1 vote for every 2 that Amy would have gotten. How many people voted?

Hint: Assign a variable so you can write expressions and set up equations. What's often a useful way to assign a variable in a ratio problem?

Answer 1

30 people

Explanation:

The ratio of Kim's votes to Amy's votes is 3:2, so Kim received 3x votes and Amy received 2x votes for some value of x. If 8 of the people had voted for Amy instead of Kim, then Kim would have 3x-8 votes and Amy would have 2x+8 votes. If this had happened, then Amy would have twice as many votes as Kim, so 2x+8=2(3 x-8).

Expanding the right-hand side gives 2x+8=6x-16.

Subtracting $2 x$ from both sides and adding 16 to both sides gives 24=4x, so x=6.

Since 3x+2x=5x people voted, the number of voters is .

Answer 2

The number of people who voted is 30 people.

Explanation:

Given:

Kim was elected class president. She received 3 votes for every 2 that Amy got.

No one else ran.

However, if 8 of the people who voted for Kim had voted for Amy instead, Kim would have received only 1 vote for every 2 that Amy would have gotten

Find:

the number of people voted

Step 1 of 1

The ratio of Kim's votes to Amy's votes is 3:2, so Kim received 3x votes and Amy received 2x votes for some value of x. If 8 of the people had voted for Amy instead of Kim, then Kim would have 3x-8 votes and Amy would have 2x+8 votes. If this had happened, then Amy would have twice as many votes as Kim, so 2x+8=2(3 x-8).

Expanding the right-hand side gives 2x+8=6x-16.

Subtracting $2 x$ from both sides and adding 16 to both sides gives 24=4x, so x=6.

Since 3x+2x=5x people voted, the number of voters is
`$5 \cdot 6=30$`.