Adrienne had a party at a local bowling alley. She spent seventy-five dollars for the lane and five dollars per person for shoes. Let c be the total cost of the lane and shoes, and let f be the number of friends at her party. Write an equation to represent the problem. Which is the dependent variable? Explain.
C = 75 + 5f.
C is the dependent variable. It depends on the value of f.
c = 75 + 5 f
cost c depends on number of friends f
This question could have been written another way around.
Lets see how many friends Adrienne is can spend 5 dollars on in addition to spending 75 on the rental for amount in her budget c
f = (c - 75)/5
NOW f depends on c
but the equation is really the same
5 f = c - 75
or
75+5f = c
To write an equation to represent the problem, we can start by breaking down the given information. Adrienne spent $75 for the lane and $5 per person for shoes. Let's use the variables c and f to represent the total cost of the lane and shoes, and the number of friends at the party, respectively.
To find the total cost, we can add the cost of the lane to the cost of the shoes for f friends. The cost for the shoes would be 5 dollars multiplied by the number of friends, which gives us 5f.
Therefore, the equation to represent the problem is: c = 75 + 5f.
In this equation, c is the dependent variable because it depends on the number of friends (f). The number of friends determines the number of shoes needed and thus affects the total cost of the lane and shoes (c).