Monroy/ Per.
7
Math
Tutorial
Problem: The math club and the science club had fundraisers to buy supplies for a hospice. The math club spent $135 buying six cases of juice and one case of water. The science club spent $110 buying four cases of juice and two cases of bottled water. How much did a case of juice cost? How much did a case of water cost?
Answer: Juice = $20 / Water = $15
Steps:
First, in order to solve this problem, you must define your variables, which in this case, are juice and water.
Ex. Juice: J.
Water: W.
The next step in solving this problem, is to set it up as a
system of equations. Although there
are multiple ways to solve this problem, I think that setting it up as a system
is the easiest, fastest and most accurate way to acquire your answer. In order to do this, you have to
construct two equations, one to represent the Math Club’s expenses and one to
represent the Science Club’s
expenses.
Ex. Math Club: 135 = 6j + w
Science Club: 110 = 4j + 2w
After you have your two equations, the third step is to solve for one of the variables with substitution. One way to do this, is to solve for “w.” (You can substitute to find “W” into either equation. In the example below, I used the Math Club equation to find “W.”)
Ex. 135 = 6j + w
-6j -6j ß Use property of equality to subtract 6j from both sides.
________________
135 – 6j = w
Now that you have the value of one of your variables, “W”, you need to solve for the other, “J”. to do this, you substitute (135-6j) in for “W”. (This can be substituted into either of the two equations, the example below is substituted into the science club’s equation.)
Ex. 110 = 4j + 2(135 – 6j) ß Use distributive property.
110 = 4j + 270 – 12j
(4j-12j = -8j) ß Combine like terms.
110 = 270 -8j ß Use property of equality to subtract 270 from each side.
-270 -270
___________
-160 = -8j ß Divide by 8 to figure what j equals.
____ ___
-8 -8
-------------------
20 = j
The last step to solving this equation is to find the final value of “W”. To do this, you substitute “J” in, to find the unknown variable, “W”. (You can also substitute “J” into either equation, the example below is substituted into the Math Club’s equation.)
Ex. 135 = 6 (20) + w
135 = 120 + w ß Use property of equality to subtract 120 from each side.
-120 -120
__________________
15 = w
* Another method to
solve this problem, is by constructing a graph.
(To do this, you graph the two linear equations on one graph, where one axis represents Water and the other represents Juice. The point of intersection represents the costs of both Water and Juice.)
