Question

smoothies for $5.

1. fill in the boxes to write a ratio that compares the cost

to the number of fruit smoothies.
$□
□ smoothies

1. suppose katie and her friends buy 6 fruit smoothies.

complete the ratio that compares the cost to the number
of fruit smoothies.
$□
6 smoothies

1. is the cost proportional to the number of fruit smoothies for

two and six smoothies? explain.

Explanation:

Step1: Identify given ratio values

The given deal is 2 smoothies for $\$5$, so the ratio is $\frac{\$5}{2 \text{ smoothies}}$

Step2: Calculate cost for 6 smoothies

First find unit cost: $\frac{\$5}{2} = \$2.5$ per smoothie.
Cost for 6 smoothies: $6 \times 2.5 = 15$, so ratio is $\frac{\$15}{6 \text{ smoothies}}$

Step3: Check proportionality

Simplify both ratios:
$\frac{5}{2} = 2.5$, $\frac{15}{6} = 2.5$. Since the unit rates are equal, they are proportional.

Answer:

1. $\frac{\$5}{2 \text{ smoothies}}$
2. $\frac{\$15}{6 \text{ smoothies}}$
3. Yes, the cost is proportional to the number of smoothies. Both ratios simplify to the same unit rate of $\$2.50$ per smoothie, meaning the cost per smoothie is constant.