Solving Systems Of Equations - High School

Sam sells two different deals of Apples and Bananas to produce stands. First deal contains 30 pounds Bananas and 40 pound Apples for a total cost of $360. The other package contains 15 pounds Banana and 10 pound Apples for $130.00. The following system of equations represent this relationship where A represents the cost of one dozen Apples and O represents the cost of one dozen Oranges:
30 B + 40 A = 360
15 B + 10 A = 130
Solve the system of equation and find the cost of one pound Banana (B) and the cost of one pound Apples (A) in dollars.

Explanation:
In order to solve the above equations with two variables A and B we must first get rid of one variable and solve in terms of the other. I will be using the method of addition and subtraction of the two equations in order to eliminate one variable and solve for the other. I will then substitute the known variable into the equation and solve for the final missing variable. Lets go:

To be able to subtract the second equation from the first, I must have change the second equation and have one of my variables either O or A equal the same coefficient as in the first equation. I have chosen to eliminate O. To do this, I must multiply the second equation by 2 . Here goes:
30 B+ 40 A = 360
(2) 15 B + 10 A = 130
So now we have :
30 B+ 40 A = 360
30 B + 20 A = 260
Now we can subtract the second equation from the first
20 A = 100
In order to solve for A, divide both sides by 20
A = 100 / 20 = $5
The cost of one pound Apples (A) = $5
To find the cost of one pound Banana (B) then substitute in the first equation :
30 B+ 40 (5) = 360
30 B + 200 = 360

Subtract 200 from both sides :
30 B +200 - 200 = 360-200
30 B = 160

Divide both sides by 30 to find B :
30 / 30 B = 160 / 30
B = $5.333

The cost of one dozen Bananas = $5.3

In order to check our work we can substitute these numbers in one of the original equations and find out if the right hand of the equation equals what is on the left. So lets check with the second equation:
30 ($5.333) + 40 ($5) = $360

$160 + $200 = $360 It checks OK

©Copyright 2007.Najwa S. Hirn. All rights reserved.