Interpreting Word Problems

Interpreting Word Problems

Interpreting Word Problems

In this lesson we will see a couple of word problems and interpret what the answers mean as we go. For Business Calculus, it is important to understand what our answers give us and what they mean.

Example 1

A small business makes cookies and sells them at the farmer's market. The function representing the monthly cost to make x number of cookies, in dozens, is 

 $C\left(x\right)\ =\ 790\ +\ 2.88x$  . 

The monthly revenue function to sell x dozen of cookies is 
 $R\left(x\right)\ =\ 6x$  .

Multiple Choice

a) Recall that the profit function, P(x), is R(x) – C(x). What is the monthly profit function for this small business?

• P(x) = 3.12x - 790

• P(x) = 3.12x + 790

Multiple Choice

b) The break-even point occurs when R(x) = C(x), or when P(x) = 0. What value of x is needed to break even? (Round your answer up.)

• 254

• 245

• 250

• 262

Open Ended

c) Interpret your answer from part (b). What does that value of x represent?

Example 2

You are planning on getting a new Samsung Galaxy S21 5G that costs $800. Straight Talk Wireless offers a 5 GB plan for $35 per month, but you need to purchase your own phone. T-Mobile offers the same plan at $70 dollars a month, but includes the price of the phone. With T-Mobile, you have a two year plan, but with Straight Talk you can change companies at any time.

Multiple Choice

a) What is the cost of using Straight Talk for x months, including the price of the phone?

• C(x) = 35x + 800

• C(x) = 35x - 800

• C(x) = 420x + 800

• C(x) = 35x

Multiple Choice

b) What is the cost of using T-Mobile for x months?

• C(x) = 70x

• C(x) = 70x - 800

• C(x) = 70x + 800

• C(x) = 840x

Multiple Choice

c) After 2 years, which company has the better deal?

• Straight Talk Wireless

• T-Mobile

Summary

Our class this semester is going to have a large number of word problems. It is important to be able to interpret these as we find our answers.

Poll

How comfortable do you feel with interpreting word problems?

• I understand this.

• I just need a bit more practice.

• This is difficult, but I understand a little.

• I am struggling with this topic.