Question

Jaxon and Lucius were selling lemonade. Jaxon and Lucius have a difference of 5 cups sold. Jaxon was selling his for $6 a cup and Lucius was selling his for $3 a cup and together they made $300 in revenue. How many cups did Jaxon and Lucius sell each?

1. Define your variables: x is ______. y is ________. (4 points)

2. Write two equations (6 points)

Solve this system of equations using all three methods: graphing, substitution and elimination.

Show all your work.

Remember your graph should match the answers for the other two methods. All answers should be identical, it's just 3 different ways of solving the same problem.



3. Solve using graphing. Include your graph with labels. (10 points)

4. Solve using substitution. Show all work. (10 points)

5. Solve using elimination. Show all work. (10 points)

6a. What is the solution? This should be written as an ordered pair. (2 points)

6b. What does the answer mean in context of the problem? In other words, explain your answer with words/labels. (3 points)

Answer 1

the points are (35,30) you may need to search a graph online i used desmos

Explanation:

1. x= Jacksons Cups y= Lucius Cups2. x - y= 5 6x + 3y = 300Substitution: 6 (y+5) + 3y = 300 6y + 30 + 3y = 300 9y = 270 dived both by 9 y=30 Sub y for other equation x - 30 = 5 add 30 to both sides x = 35 Answer: (35, 30) Graphing: x- y = 56x+ 3y = 300solve both for y y = x-5 6x + 3y = 300minus 6x from both sides the points are in y = mx + b y= 1x -5 y= -2x + 100 I will also leave the ss of the graph in the comments if you cannot see it My labels for the x-axis is Jacksons cups and y Is luscious cups. Elimination:x - y = 5 6x + 3y = 300 First I manipulated the equations by the following - 6 (x - y = 5 ) 1(6x + 3y = 300 ) -6x + 6y = -30 6x + 3y = 300 The 6 x's cancel and add the y's and real numbers together 9y = 270 dived both by 9 y= 30 Sub y for other equation x - 30 = 6 add 30 to both sides x= 30 The points are (35, 30) The solution is (35,30)They represent how many cups they sold. 35 is Jackson cups and 30 is Lucious's cups