Question

One day a store sold 36 sweatshirts. White ones cost​ $10.95 and yellow ones cost $11.50. In​ all, ​$404.65 worth of sweatshirts were sold. How many of each color were​ sold?
The store sold ____ white sweatshirts

Answer 1

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:

$y+w=36$

And since each white sweatshirt cost $10.95 and each yellow sweatshirt cost $11.50 and the total profit was $404.65:

$10.95w+11.5y=404.65$

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:

$y=36-w$

Substitute this into the second:

$10.95w+11.5(36-w)=404.65$

Distribute:

$10.95w+414-11.5w=404.65$

Simplify:

$-0.55w=-9.35$

Divide both sides by -0.55:

$w=17$

So, 17 white sweatshirts were sold.

Using the modified equation, substitute:

$y=36-(17)=19$

Therefore, 17 white sweatshirts were sold and 19 yellow sweatshirts were sold.