A relief organization supplies blankets cots and lanterns to

A relief organization supplies blankets, cots, and lanterns to victims of fires, floods, and other natural disasters. One week the organization purchased 25 blankets, 10 cots, and 5 lanterns for a total cost of $1500. The next week, at the same price, the organization purchased 5 blankets, 20 cots, and 5 lanterns for a total cost of $1850. The next week, at the same price, the organization purchased 25 blankets, 30 cots, and 5 lanterns for a total cost of $3000. Find the cost of each item. blanket $ cot $ lantern $

Solution

Let the cost of each blanket be $x, each cots be $y and each lantern be $z
25x+10y+5z = 1500 ....eqn 1
5x+20y+5z = 1850 ...eqn 2
25x+30y+5z = 3000 ..eqn 3

eqn3-eqn1:
20y = 3000-1500
y = 75

eqn1-eqn2:
20x - 10y = 1500-1850
20x-10y = -350
20x - 10*75 = -350
x =20

put value of x and y in eqn 1
25*20 + 10*75 + 5z= 1500
z = 50
Answer:
cost of ,
blanket = $20
cots = $75
lantern = $ 50