Question

Ms. Chang’s class decides to order posters that advertise a walkathon to raise money for a local charity. Ichiro obtains quotes from two different companies.Clear Prints charges $2 per poster. Posters by Sue charges $15 plus $.50 per poster.a. For each company, write an equation Ichiro could use to calculate the cost for any number of posters.b. For what number of posters is the cost the same for both companies? Explain.c. Which company do you think the class should buy posters from? Explain your reasoning.d. If Ms. Chang’s class has an $18 budget for posters, which company do you think the class should buy posters from? If Ms. Chang donates an additional $10 for ordering posters, does it impact the decision made? What factors influenced your decision?

Answer 1

a. For each company, write an equation Ichiro could use to calculate the cost for any number of posters.

• For Clear Prints: Cost(p) = 2p

• For Sue: Cost(p) = 15 + 0.50p

b. For what number of posters is the cost the same for both companies?

• 10 posters

c. Which company do you think the class should buy posters from?

• if the number of posters is less than 10 they should use Clear prints, because it costs is lower than Sue's.

• If the number of posters is equal to 10, the cost is the same with both companies

• If the number of posters is greater than 10 they should select Sue.

d. If Ms. Chang’s class has an $18 budget for posters, which company do you think the class should buy posters from?

• Clear Print

e. If Ms. Chang donates an additional $10 for ordering posters, does it impact the decision made?

• Yes, in this case the class must order the posters from Sue.

What factors influenced your decision?

• The budget and the charges of each company/

Step-by-step explanation:

a. For each company, write an equation Ichiro could use to calculate the cost for any number of posters.

Clear prints

Call p, the number of posters. The cost is the number of posters, p. times the unit cost per poster ($2):

• Cost(p) = 2p

Sue

Using the same variable, p, for the number of posters, the cost is the flat rate, $15, plus the number of posters multiplied by the unit cost per poster, $0.50:

• Cost(p) = 15 + 0.50p

The equations fhat Ichiro could use to calculate the cost for any number of posters, are:

• For Clear Prints: Cost(p) = 2p

• For Sue: Cost(p) = 15 + 0.50p

b. For what number of posters is the cost the same for both companies?

Solve the system: equate both equations:

• 2p = 15 + 0.50p

• 2p - 0.50p = 15

• 1.50p = 15

• p = 15/1.50

• p = 10

Conclusion: For 10 posters the cost is the same for both companies.

c. Which company do you think the class should buy posters from?

It depends on the budget and the number of posters desired.

You can calculate the range in which the cost is lower by one company of the other.

You already know that if you are ordering 10 posts, the cost is the same for both companies.

How much is that cost? Compute Cost (10):

• Cost(10) = $2(10) = $20

What happens if the number of posters is less or greater than 10.

Solve an inequality:

• 2p < 15 + 0.50p

• 2p - 0.50p < 15

• 1.50p < 15

• p < 15 /1.50

• p < 10

Hence,

• if the number of posters is less than 10 they should use Clear prints, because it costs is lower than Sue's.

• If the number of posters is equal to 10, the cost is the same with both companies

• If the number of posters is greater than 10 they should select Sue.

d. If Ms. Chang’s class has an $18 budget for posters, which company do you think the class should buy posters from?

In this case the decision is driven by the buget.

How may posters can the class order to pay $18?

With Clear Prints:

• 18 = 2p

• p = 18 / 2 = 9 posters

With Sue:

• 18 = 15 + 0.5p

• 0.5p = 18 - 15

• 0.5p = 3

• p = 3 / 0.5

• p = 6 posters

Then, with a budget of $18, the class should buy posters from Clear Print.

e. If Ms. Chang donates an additional $10 for ordering posters, does it impact the decision made?

Repeat the calculations:

For Clear print:

• 18 + 20 = 2p

• p = 38 / 2 = 19 posters

For Sue:

• 18 + 20 = 15 + 0.50p

• 0.50p = 38 - 15

• 0.50p = 23

• p = 23 /0.5 = 46 posters

With a budget of $38 the class can buy more posters from Sue.

What factors influenced your decision?

• The budget and the charges are the factors that influence the decision.
• Once you know the charges from each company, you can calculate the number of posters the class can order from each one, with a given budgent, and then make the best decision (economically speaking).
• The charges have two components that constitute the total cost: a flat fee (in the case of Sue) and a unit cost (in both cases).