Compare unit prices
Use a common amount and comparable products. P is the pack price, q is its quantity, b is the comparison amount and u is the price for that amount. Compare exact rates, then round the requested result
\[u=\frac{P}{q}\times b\]
- Quantities The pack quantity and comparison amount must use the same unit
- Decision Lower price per common amount means better value. Equal rates mean equal value
- Alternative rate When comparing quantity per dollar, choose the larger amount per dollar
Worked example
These packs contain the same seeds. Compare their prices per hundred grams
\[\begin{gathered}A:\ 400\text{ g for }\$3.28\\B:\ 1.4\text{ kg for }\$10.92\end{gathered}\]
- \(\displaystyle 1.4\text{ kg}=1400\text{ g}\)Use grams for both quantities
- \(\displaystyle \begin{gathered}u_A=\frac{3.28}{400}\times100\\u_A=0.82\end{gathered}\)This is A's price in dollars per hundred grams
- \(\displaystyle \begin{gathered}u_B=\frac{10.92}{1400}\times100\\u_B=0.78\end{gathered}\)This is B's price in dollars for the same amount
- \(\displaystyle 0.78<0.82\)B has the lower unit price. This comparison assumes the same quality and that the seeds will be used
Common mistakes
Comparing only pack prices
✕\(\displaystyle \begin{gathered}\text{Choose A because}\\3.28<10.92\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{Choose B because}\\0.78<0.82\end{gathered}\)
The pack quantities differ. Compare prices for the same amountEarly rounding
✕\(\displaystyle \text{Price per 100 g}=\$1.00\)✓\(\displaystyle 4.62\div700\times100=0.66\)
For the 700 g pack costing $4.62, rounding the price per gram to $0.01 gives the incorrect price of $1 per hundred grams. Keep the original division to get $0.66Difficulty levels
introCompare two packs in matching units
standardCompare up to three packs or calculate a saving for a common amount
challengeConvert mixed units before comparing prices or savings
Questions about this topic
Is the largest pack always better value?+
No. Compare prices for the same amount
Does better unit value always mean I should buy that pack?+
No. Also consider the amount needed, whole-pack costs, quality and possible waste
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 11, VCE Units 1 & 2, General Mathematics, chapter 1: Percentages and ratios
In this chapter
Convert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1A Percentages: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changeAdd GST to a priceFind the GST and the pre-GST price from an inclusive priceExpress a ratio in simplest formComplete an equivalent ratioDivide a quantity in a given ratio1E Dividing in a ratio: Use one known part of a ratio to find the others1F Unitary method: Find the original amount from a percentage1F Unitary method: Use one known part of a ratio to find the othersScale a proportional quantity with the unitary methodDecide which option is the better value