Better Deal Example 2
Completion requirements
Lesson 1: Unit Pricing - Better Deal Example 2
Multimedia
A video describing making a purchasing decision taking into consideration unit price and customer need is provided.
EXAMPLE 2
Tarik wants to hang a picture in his bedroom. He goes to the hardware store to buy a kit of wall fasteners. He has the choice between an 82-piece kit, which costs $4.99 or a 435-piece kit, which costs $19.99. What is the better deal for Tarik?
Step 1: Calculate the unit price for both items
\(\begin{align} \text{unit price}&=\frac{\text{price}}{\text{number of items}} \\ \\ &=\frac{\$4.99}{82\,\text{pieces}} \\ \\ &=\$0.061\text{/piece or 6.1 cents per piece for the 82-piece set} \\ \end{align}\)
\(\begin{align} \text{unit price}&=\frac{\text{price}}{\text{number of items}} \\ \\ &=\frac{\$19.99}{435\,\text{pieces}} \\ \\ &=\$0.046\text{/piece or 4.6 cents per piece for the 435-piece set} \\ \end{align}\)
Solution
Step 1: Calculate the unit price for both items
\(\begin{align} \text{unit price}&=\frac{\text{price}}{\text{number of items}} \\ \\ &=\frac{\$4.99}{82\,\text{pieces}} \\ \\ &=\$0.061\text{/piece or 6.1 cents per piece for the 82-piece set} \\ \end{align}\)
\(\begin{align} \text{unit price}&=\frac{\text{price}}{\text{number of items}} \\ \\ &=\frac{\$19.99}{435\,\text{pieces}} \\ \\ &=\$0.046\text{/piece or 4.6 cents per piece for the 435-piece set} \\ \end{align}\)
Step 2: Determine the better deal accounting for unit price, quality, and quantity.
Tarik should choose the 82-piece kit. By unit price, the 435-piece kit is cheaper (4.6 cents/piece compared to 6.1 cents/piece) however, since Tarik is only hanging one picture, he probably doesn't need 435 pieces, and the 82-piece kit would be enough to complete the task.
or
Tarik should choose the 435-piece kit. By unit price, the 435-piece kit is cheaper (4.6 cents/piece compared to 6.1 cents/piece) and Tarik could use the left-over pieces for other home improvement projects he might do at a later date.
| Both answers can be considered correct because of the explanations given. |
Points to Ponder
When calculating unit price, sometimes answers are rounded to three decimal places. This is often done when dealing with large quantities of an item, where a difference in unit price is not easily seen until the third decimal place. In Example 1, if you were to round to two decimal places, the small kit would be 6 cents per item and the large kit 5 cents per item. The difference between the unit price of the two kits would be $0.01 or 1 cent. Look at the chart below to see the difference between rounding a unit price to two decimal places vs. rounding to three decimal places when the number of items becomes quite large.
| Number of items purchased | Rounded to 4.6 cents per unit | Rounded to 6.1 cents per unit | Cost difference | Rounded to 5 cents per unit | Rounded to 6 cents per unit | Cost difference |
| 100 | $4.60 | $6.10 | $1.50 | $5.00 | $6.00 | $1.00 |
| 1 000 | $46.00 | $61.00 | $15.00 | $50.00 | $60.00 | $10.00 |
| 10 000 | $460.00 | $610.00 | $150.00 | $500.00 | $600.00 | $100.00 |
Now, it is your turn! Complete the questions in your Chapter 1, Lesson 2 Practice Makes Perfect that refer to Calculating the Better Deal.
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