Jen bought some sesame bagels and some plain bagels. the ratio of the numbers of sesame bagels to the number of plain bagels is 1: 3 .

a. what is the fraction of the bagels that are plain.
b. what percent of the bagels are plain.
c. if jill bought 2 dozen bagels, how many of each type of bagel did she buy.

A. What is the fraction of the bagels that are plain?

Sesame bagels: plain bagels = 1 : 3
This means that 1/3 of the bagels are sesame.
Therefore, you know that 2/3 of the bagels are plain, as Jen bought only these two types of bagels.

B.  What percent of the bagels are plain?

From Part A, we know that 2/3 of the bagels are plain.  To find the decimal approximation, we just divide the numerator by the denominator.

2/3 ≈ 0.67

0.67 as a percentage is 67%.

Therefore, 67% of the bagels are plain.

C. If Jen bought two dozen bagels, how many of each type of bagel did she buy?

We know that a dozen bagels is 12 bagels.
Because Jen bought two dozen bagels, she has 24 total bagels.

We know that the ratio of sesame to plain bagels is 1:3.
We set up an equation to model this ratio, letting x represent the number of unknown bagels.

1x + 3x = 24

When we combine like terms, we get the equation:
4x=24

When we divide both sides by 4, we get our

x=6

Now we substitute our known variable back into the equation for x.

1(6) = sesame 
3(6) = plain
Together, these amounts equal 24 bagels.
After multiplying, we find out that Jen bought a total of 6 sesame bagels and 18 plain bagels.