Question 953110: It looks like someone has already solved a similar problem with Matrices. I wanted to solve this without that. Here is the question
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 15 lanterns for a total cost of $1750. The next week, at the same prices, the organization purchased 25 blankets, 20 cots, and 25 lanterns for a total cost of $2950. The third week, at the same prices, the organization purchased 25 blankets, 30 cots, and 5 lanterns for a total cost of $3100. Find the cost of one blanket, the cost of one cot, and the cost of one lantern. I keep getting 4.8, for the blanket so I must be doing something wrong.
So far I have this..
25b+10c+15L=1750
25b+20c+25L=2950
25b=30c+5L=3100
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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 15 lanterns for a total cost of $1750. The next week, at the same prices, the organization purchased 25 blankets, 20 cots, and 25 lanterns for a total cost of $2950. The third week, at the same prices, the organization purchased 25 blankets, 30 cots, and 5 lanterns for a total cost of $3100. Find the cost of one blanket, the cost of one cot, and the cost of one lantern. I keep getting 4.8, for the blanket so I must be doing something wrong.
So far I have this..
25b + 10c + 15L = 1750
25b + 20c + 25L = 2950
25b + 30c + 5L = 3100
;
We can do this using elimination
subtract the 1st equation from the 2nd equation
25b + 20c + 25L = 2950
25b + 10c + 15L = 1750
-----------------------subtraction eliminates b
0 + 10c + 10L = 1200
simplify divide by 10
c + L = 120
:
Subtract the 2nd equation from the 3rd equation
25b + 30c + 5L = 3100
25b + 20c + 25L = 2950
----------------------- eliminates b
0 + 10c - 20L = 150
simplify, divide by 10
c - 2L = 15
:
Subtract the above equation from the 1st 2 unkown equation
c + L = 120
c -2L = 15
--------------Subtraction elimnates c, find L
0 + 3L = 105
L = 105/3
L = $35 for the lantern
then using c + L = 120
c + 35 = 120
c = $85 for a cot
and using 25b + 20c + 25L = 2950
25b + 20(85) + 25(35) = 2950
25b + 1700 + 875 = 2950
25b + 2575
25b = 2950 - 2575
25b =
b = 375/25
b = $15 for a blanket,
You confirm this by putting these values in the other two equations
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