business sold 21 sweatshirts.red sweatshirts each cost $19.95, while other colors each cost $24.95. $463.95 worth of sweatshirts ere sold. How many were sold?

Question

I can never understand the problem 

Answer 1

If 21 red sweatshirts were sold, totalling 463.95 at two prices $19.95, and $24.95 each, this gives the following equations (x is red, y is other):

 

x*19.95+y*24.95=$463.95

 

x+y=21

 

To solve for each, solve second equation for x and insert into the first equation:

 

x=21-y

 

(21-y)*19.95 + y*24.95=463.95

 

Simplify:

 

418.95 - y*19.95 + y*24.95=463.95

 

5*y = 45

 

y=9

 

Substitute back in to get x.

 

x=21-9

x=12

 

Answer:  12 red and 9 other color sweatshirts.

Answer 2

r=# of red sweatshirts sold

21-r=# of other color sweatshirts sold

19.95r+24.95(21-r)=463.95

19.95r+523.95-24.95r=463.95

523.95-5r=463.95

-5r=463.95-523.95

-5r=-60

5r=60

r=60/5

r=12 red sweatshirts sold and 21-12=9 other colored sweatshirts sold

check:

12*19.95=$239.40

9*$24.95=$224.55

$239.40+$224.55=$463.95