WORD PROBLEMS INVOLVING LINEAR MODEL

Problem 1 :

The cost of a school banquet is $95 plus $15 for each person attending. Write an equation that gives total cost as a function of the number of people attending. What is the cost for 77 people?

Solution

Problem 2 :

In 1980 the average price of a home in Brainerd County was $97,000. By 1986 the average price of a home was $109,000. Write a linear model for the price of a home, P, in Brainerd County as a function of the year, t. Let t = 0 correspond to 1980.

Solution

Problem 3 :

Roman paid $150 to join a handball club. He pays an additional $15 every time he uses one of the club's handball courts. Write an equation that describes Roman's total cost for playing handball as a function of the number of times he plays.

Let C = the total cost and n = the number of times he plays.

Solution

Problem 4 :

A sunflower in Julia Rosario's garden was 12 centimeters tall when it was first planted. Since then, it has grown approximately 0.6 centimeters per day. Write an equation expressing the sunflower's height, H, in terms of the number of days, d, since it was planted.

Solution

Problem 5 :

Billy plans to paint baskets. The paint costs $14.50. The baskets cost $7.25 each. Write an equation that gives the total cost as a function of the number of baskets made. Determine the cost of four baskets.

Solution

Problem 6 :

A real estate sales agent receives a salary of $250 per week plus a commission of 2% of sales. Write an equation that gives the weekly income y in terms of sales x.

Solution

Problem 7 :

If a large factory sells its new gadgets for $5 each, it can sell 1050 per month, and if it sells the same gadgets for $9, it will sell 900 per month. Assuming the relationship between price and sales is linear, predict the monthly sales of gadgets to the nearest whole number if the price is $12.

Solution

Problem 8 :

The graph for a stable that charges a $20 flat fee plus $10 per hour for horseback riding is shown below.