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.
.
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
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    - 43n = -86
        n = $2 (cost of a napkin)
.
Cost of tablecloth:
 t + 6n =  24
 t + 6(2) =  24
 t + 12 =  24
 t = $12