work question

[janewatts3]

A machine shop can manufacture either 17 crankshafts or 30 gears in 10 hours of production time, but not both. Crankshafts sell for $190 apiece and gears sell for $100 apiece.

Quantity A

The value of the inventory produced by the machine shop in 270 minutes of producing crankshafts

Quantity B

The value of the inventory produced by the machine shop in 285 minutes of producing gears



I was doing this problem on the assumption that you can't value a partial crankshaft or gear, that they should be rounded down to nearest whole number. In the end, the value in Quantity A is 7.65 cranks and Quantity B is 14.25. Since those are counted items, I thought I should round down to real numbers instead of counting .25 of a gear, etc. That caused me to get this wrong even though all of my math was right. How would I know to include partial parts for the final inventory $ value? Thanks!

[tommywallach]

Hey There,

Is this our question, or an official question, or from another source? You are absolutely right that you couldn't sell a partial gear or crankshaft, so you would round down. I'll solve it as I see it:

Quantity A

They make 1.7 crankshafts per hour, so in 4.5 hours, they would make 7.65 crankshafts, which is 7 crankshafts, which is worth $1453.50.

Quantity B

They make 3 gears per hour, or one gear every 20 minutes. In 285 minutes, they would produce 14 gears, which is worth $1400.

The answer is A. If that's not the posited answer, then the question is busted.

-t