Question

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

Answer 1

Answer:

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.