A band group is having a carwash fundraiser to earn money. The group spent $25 on soap. Each car is charged $7.

Question

Let c represent the number of cars and a represent the amount of money earned.
Which variable is the independent variable and which variable is the dependent variable?
(1 point)
c (number of cars)

Dependent
Variable
a (amount of money earned)
Independent
Variable
A band group is having a carwash fundraiser to earn money. The group spent $25 on soap. Each car is charged $7.
Let c represent the number of cars and a represent the amount of money earned.
Write an equation that shows the relationship.
(2 points)
Check Answer
A band group is having a carwash fundraiser to earn money. The group spent $25 on soap. Each car is charged $7.
Let c represent the number of cars and a represent the amount of money earned.
If the band group washed 40 cars, how much money did they earn? Solve and show all work to earn full credit.
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Answer 1

To answer your questions step by step:

Independent and Dependent Variables

In this scenario:

• Independent Variable (c): The number of cars washed (c) is independent because it can vary freely based on how many cars the group chooses to wash.
• Dependent Variable (a): The amount of money earned (a) is dependent on the number of cars washed; it changes in response to how many cars are washed.

Equation

To write an equation that shows the relationship, we take into account that the money earned is calculated based on the number of cars washed and the charge per car:

1. Each car earns $7.
2. Therefore, the money earned from washing c cars would be \( 7c \).
3. However, since the band group spent $25 on soap, we need to account for that expense in the equation.

Thus, the equation relating the money earned (a) to the number of cars washed (c) can be written as:

\[ a = 7c - 25 \]

Calculating Money Earned

If the band group washed 40 cars, we can substitute \( c = 40 \) into the equation to find the amount of money earned.

1. Substitute \( c = 40 \) into the equation:

\[ a = 7(40) - 25 \]

2. Calculate \( 7 \times 40 \):

\[ a = 280 - 25 \]

3. Finally, subtract the cost of soap from the total earnings:

\[ a = 255 \]

Therefore, if the band group washed 40 cars, they earned $255.

Summary

• Independent Variable: c (number of cars)
• Dependent Variable: a (amount of money earned)
• Equation: \( a = 7c - 25 \)
• Earnings from washing 40 cars: $255.