Answer:
17 white sweatshirts were sold and 19 yellow sweatshirts were sold.
Step-by-step explanation:
Let w represent the number of white sweatshirts sold and y represent the number of yellow sweatshirts sold.
We can write a system of equations to represent the situation.
Since the store sold a total of 36 sweatshirts, the sum of the white and yellow sweatshirts must total 36. So:
[tex]y+w=36[/tex]
And since each white sweatshirt cost $10.95 and each yellow sweatshirt cost $11.50 and the total profit was $404.65:
[tex]10.95w+11.5y=404.65[/tex]
Solve the system. I'll use substitution this time (though elimination will work just as perfect). From the first equation, subtract w from both sides:
[tex]y=36-w[/tex]
Substitute this into the second:
[tex]10.95w+11.5(36-w)=404.65[/tex]
Distribute:
[tex]10.95w+414-11.5w=404.65[/tex]
Simplify:
[tex]-0.55w=-9.35[/tex]
Divide both sides by -0.55:
[tex]w=17[/tex]
So, 17 white sweatshirts were sold.
Using the modified equation, substitute:
[tex]y=36-(17)=19[/tex]
Therefore, 17 white sweatshirts were sold and 19 yellow sweatshirts were sold.
