Word Problems: Sales Items: Example 1

Help on this type of problem.

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Sales item problems are similar to the coin problem.
Consider the sale of two types of items. An appliance store sells two types of units at prices of $500 and $750. In one week, the total sales of the two types was 28 units, and the receipts were $16000.
We want to express the receipts in terms of the number of $500 units sold.
Express the receipts, R, in terms of the numbers and prices.

R = (# of cheaper units * price of cheaper unit)
+ (# of expensive units * price of expensive unit).

Let x = # of cheaper units.
Express the # of expensive units in terms of x and the total sales.

Since 28 units were sold in total,
28 = x + (# of expensive units), or # of expensive units = 28 – x

Now express the receipts in terms of x.

R = x * 500 + (28 – x) * 750

Distribute to remove parentheses.

R = 500 * x + 21000 – 750 * x

Collect the x terms.

R = – 250 * x + 21000

If $16000 were received for the sale of these units, include that data in the equation.

16000 = – 250 * x + 21000

Subtract 21000 from both sides.

16000 – 21000 = – 250 * x +21000 – 21000
Or
– 5000 = – 250 * x

Divide both sides by – 250.

, or
20 = x

Interpret this result.

20 units were sold for $500 and
28 – 20 = 8 units were sold for $750.

Check this result.

We'll use our receipts equation:
R = 20 * $500 + 8 * $750, or
R = $10,000 + $6000 = $16000
This agrees with the data in the original problem.

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