Writing 2-Variable Equations

Name ______

1. You and your friends go to the fair! At the midway, you decide to pool your money and buy a massive number of funnel cakes and corn dogs… Each funnel cake costs $3 and each corn dog costs $2. All told, you and your friends have $100.

a. Define your variables.

b. Write an equation that would accurately represent this situation.

c. Find at least 10 different combinations of funnel cakes and corndogs that would satisfy this situation. Express each combination as an ordered pair in the form (corndogs, funnel cakes).

2. George and Dan work together to wash dishes at summer camp. George washes dishes at a consistent 5 dishes per minute, and Dan washes dishes at 4 dishes per minute. They have not necessarily been working the same amount of time (their shifts are different). They have a total of 160 dishes to wash.

a. Define your variables.

b. Write an equation that would accurately represent this situation.

c. Find at least 5 different combinations of times that both George and Dan have been working that will make this situation work. Express each combination as an ordered pair in the form (number of minutes George has worked, number of minutes Dan has worked)

3. The Algebra class is starting a business selling hot chocolate! If they charge $0.75 per cup of hot chocolate, then:

a. Write an equation for the amount of money (y) they have made after they have sold some number (x) of cups of hot chocolate.

b. Find 5 different ordered pairs that would make this equation true.

c. How much money will they make if they sell:

i. 100 cups?

ii. 150 cups?

iii. 250 cups?

d. If they discover that they have made $202.50, how many cups did they sell?

4. For the Algebra class’s hot chocolate business, they do some research and determine that each cup of hot chocolate costs them $0.23 to produce (their variable cost). In addition, they have to pay the school $15 in rent for the project.

a. Write an equation for the amount of money (y) they will have to pay after they have produced some number (x) of cups of hot chocolate.

b. How much will they pay if they produce:

i. 100 cups?

ii. 150 cups?

c. If the class has exactly $63.30 to spend, how many cups of hot chocolate can they produce?