# Derek earns money for every bucket of golf balls he collects at the golf course. Which equation can he use to determine how much money he earns?

embizze | Certified Educator

Derek earns money for every bucket of golf balls he collects at the golf course. Which equation can he use to determine how much money he earns?

Taking the question as is, this appears to be a direct variation model. In a direct variation, y=kx, where x is the independent variable, y the dependent variable, and k the constant of variation. Here x represents the number of buckets of balls, y the total amount earned, and k the constant rate of pay for a bucket of balls.

For example, if Derek is paid \$2 per bucket, the total pay received can be modeled as y=2x, with x representing the number of buckets.

The situation can be more complicated:

(1) If Derek is paid a set fee for showing up, and an additional amount per bucket of balls this could be modeled as a linear relationship y=mx+b. Here y is the total amount paid, m is the set rate for a bucket of balls, x is the number of buckets of balls collected, and b represents the set amount paid for being at the course.

(2) Derek could be paid on a sliding scale of some sort. For instance, he might be paid one rate for the first 10 buckets, another rate for the second 10 buckets, etc...

(3) Derek could even be paid on an exponential rate, as the last few buckets of balls found are harder to find than the first few.

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The best answer for the information given is to model the situation with y=kx. y is the total amount paid, x is the number of buckets retrieved, and k is the set rate (constant) paid per bucket of balls.

On a multiple choice question, you would probably be given two of the pieces of information and asked to solve for the third.

nisarg | Student

b is the number of buckets and m is the amout of money he gets per bucket

so m*b= the amount of money he gets

mchandrea | Student

The question is a bit vague since no specific number was given. For any unknown with a constant variable you can use the formula y = kx. Where k is the constant and x is the changing variable. In this case, we can say that k is equal to how much will be given to Derek per bucket; and x will be how many buckets Derek could could actually collect.

For example, let's say hypothetically, Derek is paid 4\$ per bucket, and every Monday he picks up a total of 5 buckets, 6 buckets every Tuesday and 7 buckets every Wednesday.

y = kx

Monday y= 4*5 = 20\$

Tuesday y = 4*6 = 24\$

Wednesday y= 4*7 = 28\$

So for 3 days Derek would earn a total of \$72

okay so he earns X amount of dollars for every bucket of golf balls. we do not know the amount he earns so lets substitute that with a variable X, and we also do not know how many buckets he has collected, so lets substitute that with Y. in order to figure out how much money he makes, you have to simply multiply X and Y. because for every bucket,y, he gets X amount of dollars, so the equation would look something similar to