Algebra 2 Word Problem- need help with finding equations

Question

The cheerleading team sells sun products as a fundraiser to defray camp expenses. Kara sells 31 bottles of sunscreen and 16 tubes of lip balm and raises $69.45. Macy sells 24 bottles of sunscreen and 20 tubes of lip balm and raises $61. How much profit is raised from the sale of a single sunscreen and a single lip balm?

 

Can someone help me go step-by-step through this problem?

Answer 1

Cameron, 

 

In algebra II, you begin to learn about linear functions and x and y coordinates. I am pretty sure you guys are covering how to use elimination and/or substitution in order to recover one of the coordinates, either the x or the y. 

 

The word problem is very similar to the two-variable, two-equation set-up in linear equations. 

 

The first equation can be written like:

 

31s + 16l =$69.45, where s is the value or the amount the sun screen cost and l represent the cost of the lip balm. The cost of each item times the number of items sold should equal the amount given in the problem.

 

Thus, the second equation looks like: 

 

24s + 20l = $61.00

 

I am a fan of substitution rather than elimination. You can take any equation and solve for one of the variables, but I took the second equation and solved for the sunscreen amount. 

 

The equations is: 

 

31($61 - 20l/24) + 16l = $69.45 

 

From this equation we get: 

 

l = $0.95

 

thus, s = $1.77 

 

this should be the profit amount as the problem did not explicitly indicate the whole sale price.

 

Let me know if you have any questions.

Answer 2

Allow x to equal the profit from the sunscreen and y to equal the profit from the lip balm.  Then:

 

Kara:   31x + 16y = 69.45

 

Macy:   24x + 20y = 61.00

 

This system of equations in 2 variables can be solved via elimination.

 

Multiple the equations by 10 and 8 to get the same coefficient for y.

 

10(31x + 16y) = 10(69.45)  

  8(24x + 20y) =   8(61.00)

 

310x + 160y = 694.50

192x + 160y = 488.00

 

Subtract the bottom equation from the top and solve for x.

 

118x = 206.50

 

x = 206.50/118 = 1.75

 

Substitute the value for x into one of the original equations and solve for y.

 

31(1.75) + 16y = 69.45

 

54.25 +16y = 69.45

 

16y = 15.20

 

y = .95

 

Therefore they made $1.75 for the sale of each sunscreen and $0.95 for each lip balm.