Question 133662
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 = {{{((16.20 - 20x))/10}}}
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