# Math word problem that states t-shirts are $10 each and sweatshirts are$15 each, if 100 items were sold and they raised $1120, how many sweatshirts were sold, how would i set up this problem Wierzycaz 2020-11-01 Answered Math word problem that states t-shirts are$10 each and sweatshirts are $15 each, if 100 items were sold and they raised$1120, how many sweatshirts were sold, how would i set up this problem
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SchulzD
x=number of sweatshirts sold
f(x)=the total amount of money raised by the sale
So the number of t-shirts sold would be the total number of items sold subtracted by the number of sweatshirts sold or (100-x)
So we can model this by the function:
f(x)=15x+10(100-x)
Now just plug in the money raised that is given in the question (1120)
1120=15x+10(100-x)
The final step is to solve, I would plug this into my graphing calculator:
go to y=
input the functions y=1120 and into y2 input y=15x+10(100-x)
The answer is the x value at the point of intersection.
You can also solve algebraically:
1120=15x+10(100-x)
FOIL (factor) 10(100-x)
which gives you 1120=15x+1000-10x
subtract 1000 from both sides
120=15x-10x
simplify
120=5x
divide both sides by 5 which gives the answer:
$x=\left(\frac{120}{5}\right)$