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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.

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TaeKwonDoIsDead

Answer:

436 items

Step-by-step explanation:

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

[tex]A=\frac{k}{B}[/tex]

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

For this problem, we can write the ratio as:

[tex]N=\frac{k}{C}[/tex]

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

[tex]N=\frac{k}{C}\\480=\frac{k}{4.90}\\k=4.90*480\\k=2352[/tex]

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:

[tex]N=\frac{k}{C}\\N=\frac{2352}{5.40}\\N=435.55[/tex]

Rounding to next whole number, we have 436 items

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