Question

Proportional Relationships Homework
1. A nutrition company is marketing a low-caloric snack brownie. A serving size of the snack is 3 brownies
and has a total of 50 calories.
(c) Determine how many calories 14 brownies
would have. Round to the nearest calorie.
(d) If c represents the number of calories and b
represents the number of brownies, write a
proportional relationship involving c and b and
solve it for c.

Answer 1

Proportional relationships are used to represent direct variation

The number of calories in 14 brownies is 233, and the proportional relationship is $\mathbf{c = \frac{50b}{3}}$

Let b represents brownies and c represents calories.

So, the relationship is given as:

b : c = 3 : 50

Express as fractions

$\mathbf{\frac bc = \frac{3}{50}}$

Multiply both sides by c

$\mathbf{b = \frac{3}{50}c}$

When the number of brownies is 14, we have:

$\mathbf{14 = \frac{3}{50}c}$

Multiply both sides by 50/3

$\mathbf{14 \times \frac{50}{3} = c}$

$\mathbf{233 = c}$

Rewrite as:

$\mathbf{c = 233 }$

Make c the subject in $\mathbf{b = \frac{3}{50}c}$

$\mathbf{c = \frac{50b}{3}}$

Hence, the number of calories in 14 brownies is 233, and the proportional relationship is $\mathbf{c = \frac{50b}{3}}$

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