# write an equation for the problem.  then use the equation to answer the question. Trevor's weekly allowance is calculated using a point system. For each chore he does, Trevor gets a point.  For...

write an equation for the problem.  then use the equation to answer the question.

Trevor's weekly allowance is calculated using a point system. For each chore he does, Trevor gets a point.  For each chore he misses, he loses a point. Each point is worth \$2, and negative points mean that Trevor owes money to his parents.

If Trevor has a total of 8 assigned chores each week, how much can he expect to earn or owe using the point system.

ishpiro | Certified Educator

Let's denote the number of chores Trevor chooses to do each week by the variable x. Then, the number of chores he does not do, will be 8 - x, since he has a total of 8 assigned chores each week.

Since each chore is worth a point, and each point I worth \$2, the amount of money he earns by doing x chores is \$(2x), and the amount of money he loses by not doing (8 - x) chores is \$2(8 - x).

His total "balance" for each week, denoted by B, will then be, in dollars

B = (2x) - 2(8 - x). (Money earned - money lost.)

Simplifying this expression results in

B = 2x - 16 + 2x = 4x - 16.

The amount of money Trevor can expect to earn or owe each week is described by B = 4x - 16, where x is the number of chores.

Since x is the number of chores he chooses to do each week, it is an integer between 0 and 8:

x = 0, 1, 2, ,,,8

The possible values of his balance each week are

If x = 0 (he does not do any chores) B = 4*0 - 16 = -16. He owes his parents 16 dollars.

x = 1  B = -12

x = 2  B= -8

x = 3  B = -4

x = 4 B = 0 He neither earns nor owes money.

x = 5 B = 4 He earns 4 dollars.

x = 6 B = 8

x = 7 B = 12

x = 8 B = 16 The most money he can earn, by performing all 8 chores, is 16 dollars.

The possible amounts Trevor might owe are \$16, \$12, \$8, \$4.

He might also earn and owe nothing.

He might earn \$4, \$8, \$12, or \$16.