Question
A company produces three types of products: X, Y, and Z.
Initially, the production ratio of X to Y to Z is 5:7:8. The total production of these three products is 10,800 units. After a change in the production plan, the number of units produced for type X is increased by 25%, for type Y it is decreased by 10%, and for type Z it remains the same. What is the total production of these three products after the changes?Solution
Let the initial production of X, Y, and Z be 5k, 7k, and 8k respectively, where k is the common multiple. The total production is 10,800 units, so: 5k + 7k + 8k = 10,800 20k = 10,800 k = 540 Thus, the initial production is: X = 5 * 540 = 2700 units Y = 7 * 540 = 3780 units Z = 8 * 540 = 4320 units After the changes: X’s new production = 2700 * 1.25 = 3375 units Y’s new production = 3780 * 0.90 = 3402 units Z’s production remains unchanged = 4320 units The total production after the changes is: 3375 + 3402 + 4320 = 11,097 units Answer: e) none
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