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# At the MP Donut Hole Factory, Niraek, Theo, and Akshaj

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At the MP Donut Hole Factory, Niraek, Theo, and Akshaj are coating spherical donut holes in powdered sugar. Niraek's donut holes have radius 8 mm, Theo's donut holes have radius 10 mm, and Akshaj's donut holes have radius 12 mm. All three workers coat the surface of the donut holes at the same rate and start at the same time. Assuming that the powdered sugar coating has negligible thickness and is distributed equally on all donut holes, how many donut holes will Niraek have covered by the first time all three workers finish their current donut hole at the same time?

Nov 10, 2020

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At the MP Donut Hole Factory, Niraek, Theo, and Akshaj are coating spherical donut holes in powdered sugar. Niraek's donut holes have radius 8 mm, Theo's donut holes have radius 10 mm, and Akshaj's donut holes have radius 12 mm. All three workers coat the surface of the donut holes at the same rate and start at the same time. Assuming that the powdered sugar coating has negligible thickness and is distributed equally on all donut holes, how many donut holes will Niraek have covered by the first time all three workers finish their current donut hole at the same time?

Hello Guest!

$$\frac{N\cdot Parts}{8^2mm^2}+\frac{T\cdot Parts}{10^2mm^2}+\frac{A\cdot Parts}{12^2mm^2}\\ =\frac{N}{64}+\frac{T}{100}+\frac{A}{144}\\ =\frac{N}{16}+\frac{T}{25}+\frac{A}{36}\\ = \frac{900N+576T+400A}{14400}\cdot \frac{Parts}{mm^2}$$

In the period in which Akshaj 400 and Theo 576 coated donut holes,

Niraek coated 900 donut holes.

!

Nov 10, 2020
edited by asinus  Nov 10, 2020
edited by asinus  Nov 25, 2020