MODELLING WITH LINEAR FUNCTIONS WORKSHEET

Problem 1 :

Jimmy is having a birthday party at the zoo. The zoo has a fixed fee for birthday parties, plus a fee per person. Jimmy is told the total charge for 10 people, including himself, would be $97.50 and the total charge for 20 people, including himself, would be $175. Determine the:

a) independent and dependent variables

b) rate of change

c) initial value

d) the total charge for 17 people

e) the number of people who could come for $500

Solution

Problem 2 :

Jimmy is driving home from a vacation. His car is on cruise control so he maintains a constant speed. After 3 hours of driving, he is 740 km from home. After 6 hours, he is 461 km from home. Determine the:

a. independent and dependent variables

b. rate of change

c. initial value

d. distance after 8 h and 15 m.

e. time it will take him to get home?

Solution

Problem 3 :

Jimmy and Karen rented cars from the same company. The company charges an initial fee plus a charge per km. Jimmy drove 240 km and was charged $59.40. Karen drove 490 km and was charged $74.40.

Determine the:

a. rate of change

b. initial cost

c. the charge after 837km

d. the number of km you can drive for $200

Solution

Problem 4 :

An insurance company has an initial charge to insure jewelry, plus a charge per dollar value of the jewelry. A ring with a value of $3500 costs $189.50 to insure. A ring with a value of $5900 costs $297.50 to insure.

Determine the:

a. Rate of Change

b. Initial charge

c. Cost to insure a $12000 ring

d. The value of a ring you could insure for $100

Solution

Problem 5 :

A school decides to sell t-shirts to raise money. If they sell 20 shirts, they will lose $30. If they sell 100 shirts, they will make $650.

Determine the:

a. rate of change

b. initial value

c. number of shirts they need to sell to break even

Solution

Problem 6 :

Lanny got a short term job selling computers. He is paid on commission. In order to impress customers, he bought a few nice suits. If he has $20000 in sales, he will lose $140. If he has $30000 in sales, he will make a $90 profit.

Determine the:

a. rate of change and initial value

b. the amount he needs to sell to break even

c. The amount he needs to sell in order to make $1000 profit

Solution