Systems of Equations

Question

Jessica sells T-shirts and sweatshirts on her Etsy store. In January, she sold 26 shirts and 20 sweatshirts for a total of $72. In March, she sold 52 shirts and 30 sweatshirts for a total of $1224. How much does she charge for each t-shirt and sweatshirt?

Answer 1

26T + 20S = 72

52T + 30S = 1224

multiply the first equation by 2 and subtract the 2nd equation from it

52T + 40S = 144

52T +30S = 1224

10S = -1080

S = -108 = negative $108 for a sweat shirt. They're paying you to take them.

26T = 72-20(-108) = 72+2160 = 2232 = $2,232 for a T-shirt, more than virtually anyone would pay

odds are there's a mistake in the problem. You may have copied it wrong. Maybe you meant $122.40 for the 52 T-shirts and 30 sweatshirts? March purchases are roughly twice January's, so expect total sale revenue to be about twice also, but a little less as 30 isn't twice 20.

If March's sales were $122.40, then the two equations would

be:

26T + 20S = 72, when multiplied by 2 would be:

52T + 40S = 144, subtract

52T+ 30S = 122.4 to get

10S = 21.6 = $21.60 per sweat shirt

26T = 72 - 20(21.6) = 72 - 43.2 = 28.8

T = 28.8/26 = 14.4/13 = about 1.11 or $1.11 per T shirt

If you tried graphing the originally given numbers, you'd see the lines intersect in the 4th quadrant with a highly negative number for T shirts/

Answer 2

Are you sure the numbers given are correct because after setting up two simultaneous equations I get a negative result for sweatshirts? I am assuming there have been no price changes over the interval of time.