To determine the production rate of the old machine, we first calculate how many boxes it produced in one hour.
The old machine produced 280 boxes in 4 hours:
\[ \text{Production rate of old machine} = \frac{280 \text{ boxes}}{4 \text{ hours}} = 70 \text{ boxes per hour} \]
Next, we calculate how many boxes the old machine would produce in 8 hours:
\[ \text{Boxes produced by old machine in 8 hours} = 70 \text{ boxes/hour} \times 8 \text{ hours} = 560 \text{ boxes} \]
It is given that the new machine produced 56 more boxes than the old machine in the same time. Thus:
\[ \text{Boxes produced by new machine in 8 hours} = 560 \text{ boxes} + 56 \text{ boxes} = 616 \text{ boxes} \]
Now, we need to calculate the production rate of the new machine:
\[ \text{Production rate of new machine} = \frac{616 \text{ boxes}}{8 \text{ hours}} = 77 \text{ boxes per hour} \]
Now let's evaluate the given options:
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The new machine can produce 14 boxes an hour.
- False. The new machine produces 77 boxes per hour.
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The equation y = 77x represents the production rate of the new machine.
- True. This indicates that y (the total production) is equal to 77 times x (the number of hours).
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The equation y = 84x represents the production rate of the new machine.
- False. The production rate is 77 boxes per hour, not 84.
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The new machine can produce 7 more boxes an hour than the old machine.
- True. The old machine produces 70 boxes per hour, and the new machine produces 77 boxes per hour; the difference is 77 - 70 = 7.
Based on this analysis, the correct answers are:
- The equation y = 77x represents the production rate of the new machine.
- The new machine can produce 7 more boxes an hour than the old machine.
1 answer