A production plant manufactures computer chips and packs them into five boxes: A, B, C, D, and E, with each box containing 20 chips. In three of these boxes, the chips weigh 100 g each, while in the remaining two boxes, the chips weigh 90 g each. One chip is selected from box A, two from box B, four from box C, eight from box D, and sixteen from box E. If total weight of these selected chips amounts to 2920g, then which boxes containing the 90g chips
Question
A production plant manufactures computer chips and packs them into five boxes: A, B, C, D, and E, with each box containing 20 chips. In three of these boxes, the chips weigh 100 g each, while in the remaining two boxes, the chips weigh 90 g each. One chip is selected from box A, two from box B, four from box C, eight from box D, and sixteen from box E. If total weight of these selected chips amounts to 2920g, then which boxes containing the 90g chips
Solution
To solve this problem, we need to set up equations based on the information given and then solve for the unknowns.
Let's denote the boxes with 100g chips as X and the boxes with 90g chips as Y.
From the problem, we know that:
1 chip from box A + 2 chips from box B + 4 chips from box C + 8 chips from box D + 16 chips from box E = 2920g
We also know that there are 3 boxes of X and 2 boxes of Y.
So, we can set up the following equations:
A + 2B + 4C + 8D + 16E = 2920 (equation 1)
And since we know that there are 3 boxes of X and 2 boxes of Y, we can also write:
A + B + C = 3X (equation 2)
D + E = 2Y (equation 3)
We know that X = 100g and Y = 90g, so we can substitute these values into equations 2 and 3:
A + B + C = 300 (equation 2)
D + E = 180 (equation 3)
Now we can substitute equations 2 and 3 into equation 1:
300 + 180 = 2920
This simplifies to 480 = 2920, which is not possible.
Therefore, there must be a mistake in the problem as it is not possible to get a total weight of 2920g with the given conditions.
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