Question

Fill in the blanks to express the quantities given in ratio language. Ratios must be expressed in simplest form.

\text{Number of Votes Cast for Each Candidate:}

Number of Votes Cast for Each Candidate:

Candidate Votes

Candidate A 35

Candidate B 49

Candidate C 28


For every (blank)

votes cast for Candidate B, there were (blank )

votes cast for Candidate A.

Answer 1

The ratio of votes for Candidate B to Candidate A, in simplest form, is 7:5, meaning for every 7 votes for Candidate B, there are 5 votes for Candidate A.

Step-by-step explanation:

To express the quantities given in ratio language, we must first understand that a ratio compares two quantities, which can be written as fractions, with a colon, or with the word "to." In this case, we're comparing the number of votes cast for Candidate B to the number of votes cast for Candidate A. Candidate A received 35 votes, while Candidate B received 49 votes. To simplify this ratio to its simplest form, we find the greatest common divisor (GCD) of the two numbers, which in this case is 7. We divide each number by 7, yielding:

• 35 ÷ 7 = 5 for Candidate A
• 49 ÷ 7 = 7 for Candidate B

Thus, the simplified ratio of votes cast for Candidate B to votes cast for Candidate A is 7:5. In other words, for every 7 votes cast for Candidate B, there were 5 votes cast for Candidate A.

Answer 2

For every 7 votes cast for Candidate B, there were 5 votes cast for Candidate A.

Step-by-step explanation:

Given:

Candidate Votes

Candidate A 35

Candidate B 49

Candidate C 28

To find:

For every (blank) votes cast for Candidate B, there were (blank ) votes cast for Candidate A

Solution:

First we have to find the ratio of B and A

B : A

49 : 35

Now lets simplify the above ratio:

reduce the ratio using greatest common factor (GCF).

Use factorization method:

Write the numbers 35 and 49 as the product of their divisors.

The factors of 35 are: 1, 5, 7, 35

This means 35 is divided by 1, 5, 7 and 35 itself

The factors of 49 are: 1, 7, 49

This means 49 is divided by 1, 7 and 49 itself

Both have 7 common in them

Hence the greatest common factor is 7.

Next, divide both terms i.e. 35 and 49 by the greatest common factor, 7

49 / 7 = 7

35 / 7 = 5

The ratio 49 : 35 can be reduced to lowest terms by dividing both terms by the greatest common factor GCF = 7

So,

49 : 35 = 7 : 5

Hence

For every 7 votes cast for Candidate B, there were 5 votes cast for Candidate A.