USING SUBTITUTION
By Nia Adams, Rosa L. Parks School of Fine and Performing Arts
Samantha is selling Eastside High School gear for her
basketball team's fundraiser.
On the first day she sells 4 t-shirts and 2 sweatpants for a total of $98.
On the total second day, Samantha sells 6 t-shirts and 4 sweatpants for a total of $165.
What is the cost for someone who wants to purchase
2 t-shirts and a pair of sweatpants?
To solve this problem, you have to split it into multiple steps (by days) and set up equations using
the process of substitution.
For day one, the equation you would have to set up is
4x+2y= $98
x symbolizes the t-shirts and y symbolizes the sweatpants.
For the second day,
the equation you would have to set up is
6x+4y= $165
First, you use the first equation to rearrange the equation into a slope- intercept form. (y=mx+b)
The formula then changes from
4x+2y= 98 to y= 2x-49
Since you now know what y equals in the first equation, you substitute the new equation into the second
formula for y.
6x+4(2x-49)= 165
Now solve for x. By the end of this step your results should be that x equals 15.50.
Now that you have the value for x, you plug it back into the first equation
4(15.5)+2y= 98
Once you solve for y, you see that y equals 18 dollars.
Now you know that each t- shirt costs
$15.50
and each pair or sweatpants costs
$18
It doesn't stop here. There is one last step. You need to answer the question completely.
Find the value of the cost of 2 t-shirts and one pair of sweatpants.
2($15.50)+18= $49
The cost for someone wanting to purchase 2 t-shirts and a pair of sweatpants would be
$49
in total.
17