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.
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.