Percentage Word Problem

[colbysmith917]

I'm having trouble with #20 in the medium section of the back of Strategy Guide #5: "A pomegranate grower packages pomegranates in 10-pound and 20-pound boxes. If the grower fills more than twice as many 20-pound boxes as 10-pound boxes, which of the following could be the percentage of pomegranates, by weight, that are packaged in 10-pound boxes?

Is picking numbers a good strategy? Or is trying to set up an equation of some sort and solve via substitution the better bet? Thank you!

[tommywallach]

Hey Colby,

Apologies. I deleted the person who responded to you early. A weird and incorrect explanation. While it's true that this could be done with algebra, my tendency would be to quickly check the range with numbers. Basically, I would want to check the percentage if I have just BARELY more than twice as many 20 pound boxes, and then WAY more than twice as many 20 pound boxes. That range of percentages will tell you what the correct answer has to be (though of course, you can logic out pretty easily that if you had WAY more than twice as many 20 pound boxes, the percentage that would be packaged in 10-pound boxes could become VERY tiny...so really the only important threshold to know is the situation where you have just BARELY more than twice as many 20 pound boxes). Checking something like eleven 20-pound boxes and five 10-pound boxes would probably suffice.

-t