SOLUTION: if 20lb of rice and 10lb of potatoes cost $16.20, and 30lb of rice and 12lb of potatoes cost $23.04, how much will 10lb of rice and 50lb of potatoes cost?

Question 133662: if 20lb of rice and 10lb of potatoes cost $16.20, and 30lb of rice and 12lb of potatoes cost $23.04, how much will 10lb of rice and 50lb of potatoes cost?
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
if 20lb of rice and 10lb of potatoes cost $16.20, and 30lb of rice and 12lb of potatoes cost $23.04, how much will 10lb of rice and 50lb of potatoes cost?
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Let "r" be cost of rice; Let "p" be cost of potatoes.
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EQUATIONS:
20r + 10p = 16.20
30r + 12p = 23.04
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Multiply 1st equation by 3; Multiply 2nd equation by 2
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60r + 30p = 3*16.2
60r + 24p = 2*23.04
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Subtract 2nd from 1st to get:
6p = 3*16.2 -2*23.04
6p = 2.52
p = 0.42 (price of a pound of potatoes is 42 cents)
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Substitute to solve for "r".
20r + 10*0.42 = 16.2
20r + 4.2 = 16.2
20r = 12
r = 0.6 (price of a pound of rice is 6 cents)
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Cheers,
Stan H.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = cost /lb of rice
Let y = cost /lb of potatoes
:
if 20lb of rice and 10lb of potatoes cost $16.20, and 30lb of rice and 12lb of potatoes cost $23.04, how much will 10lb of rice and 50lb of potatoes cost?
:
Find the cost for each using two equations:
20x + 10y = 16.20
10y = 16.20 - 20x
y =
y = 1.62 - 2x
:
30x + 12y = 23.04
Substitute (1.62-2x) for y in the above equation, find x
30x + 12(1.62-2x) = 23.04
30x + 19.44 - 24x = 23.04
6x = 23.04 - 19.44
6x = 3.6
x = 3.6/6
x = $.60 /lb for rice
:
Find the price of potatoes using the 1st equation, substitute .6 for x
20(.6) + 10y = 16.20
12 + 10y = 16.20
10y = 16.20 - 12
10y = 4.20
y = 4.20/10
y = $.42 /lb for potatoes
:
Check solution in the 2nd equation:
30(.6) + 12(.42) =
18 + 5.04 = 23.04 confirms our solution
:
But they want to know how much will 10lb of rice and 50lb of potatoes cost?
10(.60) + 50(.42) =
6.00 + 21.00 = $27.00

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