SOLUTION: a restaurant purchased 8 tablecloth and five napkins foe $106. A week later, a tablecloth and six napkins were bought for $24. Find the cost of one tablecloth and he cost of one n

Question 607286: a restaurant purchased 8 tablecloth and five napkins foe $106. A week later, a tablecloth and six napkins were bought for $24. Find the cost of one tablecloth and he cost of one napkin, assuming the same prices for both purchases.
Found 2 solutions by alicealc, nerdybill:
Answer by alicealc(293) (Show Source): You can put this solution on YOUR website!
cost of one tablecloth = T
cost of one napkin = N

8T + 5N = 106
1T + 6N = 24
Use the elimination procedure:
(multiply the second equation by 8)
8T + 48N = 192
Eliminate T:
8T + 48N = 192
8T + 5N = 106
-------------- (-)
43N = 86
N = 86/43 = 2

1T + 6N = 24
T + 6*2 = 24
T + 12 = 24
T = 24 - 12 = 12

so, the cost of one tablecloth is $12 and the cost of one napkin is $2
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
a restaurant purchased 8 tablecloth and five napkins foe $106. A week later, a tablecloth and six napkins were bought for $24. Find the cost of one tablecloth and he cost of one napkin, assuming the same prices for both purchases.
.
Let t = cost of one tablecloth
and n = cost of one napkin
then
8t + 5n = 106
t + 6n = 24
.
multiply bottom equation by -8 and combine both equations:
8t + 5n = 106
-8t - 48n =-192
-----------------
- 43n = -86
n = $2 (cost of a napkin)
.
Cost of tablecloth:
t + 6n = 24
t + 6(2) = 24
t + 12 = 24
t = $12

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