1.4 Exercises

1) Here is an expression for the cost of 7 shirts and 3 hats: [latex]𝐶 = 7𝑥 + 3𝑦[/latex].

a) What precisely does the 𝑥 represent?

b) What precisely does the 𝑦 represent?

c) What precisely does the C represent?

2) Here is an expression for the cost in (dollars) of purchasing 𝑛 pineapples and 𝑚 papayas: [latex]5𝑛 + 2𝑚[/latex].

a) What is the meaning of the number 5 in the expression?

b) Which costs more: a pineapple, or a papaya? How can you tell?

3) In an inner city school, there are 20 times as many students as teachers. Let S represent the number of students and T represent the number of teachers .

a) Explain why the equation 20S = T does NOT represent the relationship between the number of teachers and the number of students.

b) What is the correct equation for this relationship? Explain why.

4) Let P be the initial population of a town. After 10% of the town leaves, another 1400 people move into the town. The new population is 5000. Write an equation, involving P, that corresponds to this situation.

5) Write a word problem that you could use the following equations to solve. You do not have to solve it .

a) [latex]8 + x = 20[/latex]

b) [latex]3=\frac{42}{x}[/latex]

6) To make orange paint, you need to mix yellow and red paint together. For a certain shade of orange paint, you need to use  times as much yellow paint as red paint. Write an equation that relates quantities in this situation.  Be sure to define your variables clearly and correctly .

7) At the cafeteria, you can get a lunch special that offers a drink and salad. The drink costs $0.75 and a salad costs $0.25 for every ounce. Define two corresponding variables and write an equation to show how the total cost of a lunch special is related to the number of ounces of salad one gets .

8) Max was asked to write an equation corresponding to the following situation:

There are 2 times as many pencils in Antrice’s pencil box as in Keertana’s pencil box.

Max responded with the following:

A = Antrice, K = Keertana

[latex]2A = K[/latex]

Discuss Max’s work, describing and correcting any errors he has made. Explain Max’s errors and how you arrived at your answer .

9) There are F cups of flour in a bag. First, [latex]\frac{3}{8}[/latex] of the flour in the bag was used. Then [latex]\frac{1}{5}[/latex] of the remaining flour was used. At that point, there were ten cups of flour in the bag. Write an equation, involving F, that corresponds to this situation. Explain your work.

10) Describe your own situation in which two quantities vary together. Define two variables and write an equation to show how they are related.  Use a table and/or picture (e.g. bar diagram) to help show why your equation is valid.