VARIATION PROBLEMS

Here is suggested procedure for setting up and solving variation problems.

Sample: (page 22; number 10). A business found that the number of sales varies inversely with the price of the item. If a price of $9.25 each produce yearly sales of 11,550 items, lowering the price to $9.25 will produce what volume of sales?

1. Identify the variables.

Let N be the number of items sold in a year.

Let P be the price per item.

2. Set up an equation representing the relations described in the problem.

A and B represent different methods of solution.

A) N = k/P

B) Alternatively, since for any year NP =k; we can write N₁P₁ = N₂P₂.

3. Substitute the given information in the problem.

A) 11500 = k/9.25

B) 11500(9.25) =N₂(8.74)

4. In method A) solve for k: k = (9.25) 11500= 106,375. Then substitute

a second time: N = 106,375/ (8.74) = 12171.

In method B) solve for N₂ =(9.25) 11500/8.74 = 12171.