Question

The equation C = 20n + 35 represents the relationship between the cost of school volleyball uniforms, C, in dollars, and the number of uniforms ordered, n.
The school has a maximum of $600 to spend on the uniforms.

1. How many uniforms can the school buy?

2. What does the number 20 in the equation represent?

3. What does the number 35 in the equation represent?

4. The company has changed its price to $30 per uniform. How many fewer uniforms can the school
purchase for $600?

Answer 1

The equation represent a linear relation with the y-intercept

representing the amount of initial fee.

Correct response:

1. 28 volleyball uniforms

2. Price per uniform

3. Initial flat order fee

4. 10 fewer volleyball uniform

Methods used for finding the above values

The given equation that represents the relationship between the cost of school volleyball uniform is; C = 20·n + 35

Where;

C = The uniform costs

n = The number of volleyball uniform ordered

The maximum amount the school has to spend = $600

1. The number of uniforms the school can buy is given by setting C = 600 as follows;

• C = 20·n + 35

Therefore;

600 = 20·n + 35

20·n = 600 - 35 = 565

$n = \dfrac{565}{20} = \mathbf{28.25}$

Rounding down to the nearest whole number, we have;

• The number of uniforms the school can buy, n = 28 volleyball uniforms.

2. The number 20 represent the additional cost for each extra uniform, which is the unit cost therefore;

• 20 represents a $20 price per uniform.

3. The 35 in the equation represents an initial flat fee, such as an

ordering or initial fee, which is fixed.

Therefore;

• The number 35 represent the fixed cost for producing the uniforms

4. The price per uniform of $30 changes the coefficient of n from 20 to 30 as follows;

C = 30·n + 35

The number of uniforms the school can by with $600 is therefore;

$n = \dfrac{600 - 35}{30} = \mathbf{18.8 \overline 3}$

Which gives;

The number of uniforms the school can purchase at $30 per uniform is n = 18 volleyball uniforms

The difference in the number of uniforms purchased = 28 - 18 = 10

Therefore;

• The school can purchase 10 fewer uniforms at $30 per uniform

Learn more about linear equations here:

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