SOLUTION: A relief organization supplies blankets, cots, and lanterns to victims of fires, floods, and other natural disasters. One week the organization purchased 15 blankets, 10 cots, and

Algebra ->  Equations -> SOLUTION: A relief organization supplies blankets, cots, and lanterns to victims of fires, floods, and other natural disasters. One week the organization purchased 15 blankets, 10 cots, and       Log On


   



Question 1050457: A relief organization supplies blankets, cots, and lanterns to victims of fires, floods, and other natural disasters. One week the organization purchased 15 blankets, 10 cots, and 5 lanterns for a total cost of $1200. The next week, at the same price, the organization purchased 15 blankets, 20 cots, and 5 lanterns for a total cost of $1800. The next week, at the same price, the organization purchased 5 blankets, 30 cots, and 5 lanterns for a total cost of $2150. Find the cost of each item.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.15B%2B10C%2B5L=1200
2.15B%2B20C%2B5L=1800
3.5B%2B30C%2B5L=2150
Subtract eq. 3 from eq. 1 and eq. 2,
15B%2B10C%2B5L-5B-30C-5L=1200-2150
10B-20C=-950
4.B-2C=-95
and
15B%2B20C%2B5L-5B-30C-5L=1800-2150
10B-10C=-350
5.B-C=-35
Now subtract eq. 5 from eq. 4,
B-2C-B%2BC=-95-%28-35%29
-C=-60
C=60
So then working backwards,
B-60=-35
B=25
and finally,
5%2825%29%2B30%2860%29%2B5L=2150
125%2B1800%2B5L=2150
5L=225
L=45