Aceramics workshop makes wreaths, trees and sleighs for sale at christmas. a wreaths takes 3 hours, 2 hours to paint, and 9 hours to fire. a tree takes 15 hours to prepare, 3 hours to paint , and 4 hours to fire. a sleigh takes 4 hours to prepare, 14 hours to paint, and 7 hours to fire. if the workshop has 114 hours for preparation time, 15 hours for painting, and 122 hours for firing, how many of each can be made ?

w = wreaths produced t = trees produced s = sleighs produced Prep: 3w + 15t + 4s = 129 Painting: 2w + 3t + 13s = 75 Firing: 8w + 4t + 7s = 117 8w + 12t + 52s = 300 8w + 4t + 7s = 117 —————————— 8t + 45s = 183 6w + 30t + 8s = 258 6w + 9t + 39s = 225 —————————— 21t - 31s = 33 Now you have "w" gone and just the other two variables. Multiply "8t + 45s = 183" by 21, then "21t - 31s = 33" by 8, then subtract it from the first: 168t + 945s = 3843 168t - 248s = 264 ————————— 1193s = 3579 Divide each side by 1193: s = 3. (I show "8t + 45s = 183" below) and substitute s = 3 into it to find "t": 8t + 45s = 183 8t + 45*3 = 183 8t + 135 = 183 8t = 183 - 135 8t = 4 substitute s = 3 and t = 6 to find "w": 3w + 15t + 4s = 129 3w + 15*6 + 4*3 = 129 3w + 90 + 12 = 129 3w + 102 = 129 3w = 129 - 102 3w = 27 w = 9 and you're done.

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