Evergreen landscaping bought 8 tons of topsoil, 5 tons of mulch, and 2 tons of pea gravel for $2943. The next week the firm bought 5 tons of topsoil, 4 tons of mulch, and 5 tons of pea gravel for $2700. Pea gravel costs$26 less per ton than topsoil. Find the cost per ton for each item.

Question

texaschic101 · Answer

g = t - 26
8t + 5m + 2g = 2943 
8t + 5m + 2(t - 26) = 2943
8t + 5m + 2t - 52 = 2943
10t + 5m = 2943 + 52
10t + 5m = 2995

5t + 4m + 5g = 2700
5t + 4m + 5(t - 26) = 2700
5t + 4m + 5t - 130 = 2700
10t + 4m = 2700 + 130
10t + 4m = 2830

10t + 5m = 2995
10t + 4m = 2830 -->(-1)
------------------
10t + 5m = 2995
-10t - 4m = -2830 (result of multiplying by -1)
-----------------add
m = 165

10t + 5m = 2995
10t + 5(165) = 2995
10t + 825 = 2995
10t = 2995 - 825
10t = 2170
t = 217

g = t - 26
g = 217 - 26
g = 191

check....
8t + 5m + 2g = 2943
8(217) + 5(165) + 2(191) = 2943
1736 + 825 + 382 = 2943
2943 = 2943 (correct)

topsoil (t) costs $217 per ton
mulch (m) costs $165 per ton
pea gravel (g) costs $191 per ton

texaschic101 · Answer

any questions ?