Proportion Problem

[slanders09]

How do you work the potato proportion problems?

If Christina can peel 13lbs of 4.5in long potatoes in 44min, how long would it take her to peel 17lbs of 6.5in long potatoes?

Wouldn't the weight and length be inversely proportonal and jointly proportional to the time?

Eg - ((13.5lbs)(4.5in))/44min = K then solve for ((17lbs)(6.5in))/x min = K (with K determined from the previous equation)

[AuSmith]

There are a few assumptions:

1) The potatoes have the same density

2) The [unparseable or potentially dangerous latex formula] in. and [unparseable or potentially dangerous latex formula] in. potatoes have the same shape. You could even assume they are cubes if you wanted, with [unparseable or potentially dangerous latex formula] in long meaning [unparseable or potentially dangerous latex formula] in. on a side.

3) She peels skin at a constant rate.

The key is that she is peeling the surface of the potatoes. You want to find how much more/less surface area the [unparseable or potentially dangerous latex formula] in. potatoes have compared to the [unparseable or potentially dangerous latex formula] in. ones.

First find how many [unparseable or potentially dangerous latex formula] in. potatoes she has compared to the [unparseable or potentially dangerous latex formula] in. ones. The [unparseable or potentially dangerous latex formula] inchers have [unparseable or potentially dangerous latex formula] more volume, and hence [unparseable or potentially dangerous latex formula] more weight per potato. Divide [unparseable or potentially dangerous latex formula] to sort of normalize, then divide that by [unparseable or potentially dangerous latex formula]. Call [unparseable or potentially dangerous latex formula].

[unparseable or potentially dangerous latex formula] inchers should have [unparseable or potentially dangerous latex formula] more surface area, and take that much longer to peel. So, 44 minutes times how many more potatoes and times how much longer they take to peel.

[unparseable or potentially dangerous latex formula]?



Or... you can work an equivalent problem:

If you have a collection of [unparseable or potentially dangerous latex formula] in. cubes that total [unparseable or potentially dangerous latex formula] cubic inches and a collection of [unparseable or potentially dangerous latex formula] inch cubes that total [unparseable or potentially dangerous latex formula] cubic inches, how much more total surface area does the collection of [unparseable or potentially dangerous latex formula] inch cubes have?

You have [unparseable or potentially dangerous latex formula] small potatoes with [unparseable or potentially dangerous latex formula] sq. inches apiece. That's [unparseable or potentially dangerous latex formula] total square inches.

You have [unparseable or potentially dangerous latex formula] big potatoes with [unparseable or potentially dangerous latex formula] sq. inches apiece. That's [unparseable or potentially dangerous latex formula] total square inches.

Treat [unparseable or potentially dangerous latex formula] minutes as another unit of surface area. Then, it will take [unparseable or potentially dangerous latex formula] minutes to peel the big potatoes.

[slanders09]

Okay, I'm a slow learner. Here's another:

A recipe calls for the meat of 12 large lemons. If a large lemon is 4.3in long with a .25in thick rind, how many 3in long medium lemons are needed to substitute The rind on a medium lemon is also .25in.

[AuSmith]

I don't like these sorts of problems. I guess you have to think of the meat part as large enough compared to the rind that the rind has volume [unparseable or potentially dangerous latex formula]. Also, you have to assume the lemons have the same shape.

We know there is a constant [unparseable or potentially dangerous latex formula] so that given a [unparseable or potentially dangerous latex formula]-inch long lemon has volume

[unparseable or potentially dangerous latex formula],

and a constant [unparseable or potentially dangerous latex formula] so that the [unparseable or potentially dangerous latex formula]-inch long lemon has surface area

[unparseable or potentially dangerous latex formula].

We want the same amount of meat, so if we have [unparseable or potentially dangerous latex formula] large lemons and [unparseable or potentially dangerous latex formula] medium lemons,

[unparseable or potentially dangerous latex formula]

but there is no constant [unparseable or potentially dangerous latex formula] to make that equation true. The closest I can think is [unparseable or potentially dangerous latex formula]... ?

[MistaPotta]

[slanders09]

Okay, thanks! If I come across anymore proportional foodstuff problems on a calculator test, I'll be sure to ask...;)