How do I solve this problem?

Question

As treasurer of his school's FFA club, Kenny wants to buy gifts for all 18 members. He can buy t-shirts for $9 and sweatshirts for $15. The club has only $180 to spend. If Kenny wants to spend all of the club's money, how many of each type of gift can he buy?

Write a system of equations representing this problem.

Answer 1

Best solution is probably buy 15 T shirts and 3 sweatshirts

T=number of T shirts bought

S=number of sweatshirts bought

9T+15S=180

or divide by 3 to get 3T+5S=60 he could buy 20 T shirts and 0 sweat shirts, which gives every club member a T shirt with 2 left over

If he bought 12 sweat shirts and no T shirts, 6 members would get nothing, while 12 would get sweat shirts

He could buy 15 T shirts and 3 sweat shirts. That would cost $180. Everyone would get something, and 3 would get something more expensive than the T shirts of the other 15 members.

15 T shirts cost 15x9=135

3 sweatshirts cost 3x15=45

135+45=180