Question

The number of items (N) that can be purchased for a given amount of money is inversely proportional to the cost (C) of an item. If 480 items can be purchased when the cost per item is $4.90, how many items can be purchased when the cost per item is $5.40? Round to the nearest whole number.

Answer 1

436 items

Explanation:

When a quantity A is inversely proportional to another quantity B, we can write:

`A=(k)/(B)`

Where k is the proportionality constant [that we need to find]

For this problem, we can write the ratio as:

`N=(k)/(C)`

Now given N = 480 and C = 4.90, we first find k:

`N=(k)/(C)\\480=(k)/(4.90)\\k=4.90*480\\k=2352`

Now, as second step, we need this time to find N, when

C = 5.40

Note, we know know k = 2352, so we find N:

`N=(k)/(C)\\N=(2352)/(5.40)\\N=435.55`

Rounding to next whole number, we have 436 items