Question

complete the parts below. write your answers as whole numbers or fractions in simplest form. (a) justin makes fruit salad using a ratio of 6 blueberries to 14 strawberries. give two different unit rates using this relationship. one unit rate:
select
for each
select
another unit rate:
select
for each
select
(b) how many blueberries are needed if 21 strawberries are used?
blueberries

Explanation:

Part (a)

The ratio of blueberries to strawberries is \( 6:14 \). To find unit rates, we can simplify this ratio or find the rate of one quantity per unit of the other.

Step 1: Unit rate 1 (Blueberries per Strawberry)

To find blueberries per strawberry, divide the number of blueberries by the number of strawberries.

$$ \frac{6}{14} = \frac{3}{7} $$

So, one unit rate is \( \frac{3}{7} \) blueberries for each strawberry.

Step 2: Unit rate 2 (Strawberries per Blueberry)

To find strawberries per blueberry, divide the number of strawberries by the number of blueberries.

$$ \frac{14}{6} = \frac{7}{3} $$

So, another unit rate is \( \frac{7}{3} \) strawberries for each blueberry.

Part (b)

We know the ratio of blueberries to strawberries is \( 6:14 \), which simplifies to \( 3:7 \) (dividing both by 2). Let \( x \) be the number of blueberries needed when 21 strawberries are used. We set up a proportion:

$$ \frac{3}{7} = \frac{x}{21} $$

Step 1: Cross - multiply

Cross - multiply to solve for \( x \):

$$ 7x = 3\times21 $$

Step 2: Calculate the right - hand side

$$ 3\times21 = 63 $$

So, \( 7x = 63 \)

Step 3: Solve for \( x \)

Divide both sides by 7:

$$ x=\frac{63}{7}=9 $$

Answer:

s:
(a) One unit rate: \( \frac{3}{7} \) blueberries for each strawberry; Another unit rate: \( \frac{7}{3} \) strawberries for each blueberry.
(b) The number of blueberries needed is 9.