Step by step
The question
Question: which is the better buy, A: $5 for 3 pounds, or B: $7 for 4 pounds?
The amounts are different, so we can't just look at the prices.
The price for 1 pound does not come out even here.
So we make both deals the same amount.
Then we just compare the prices.
1 Write both as fractions
We write each deal as a fraction.
The money goes on top.
The pounds go on the bottom.
2 Make the same amount
3 and 4 both go into 12.
So we make both deals 12 pounds.
In A, we multiply the top and the bottom by 4.
In B, by 3.
Top and bottom get the same times, so the deal stays the same.
A: 20 dollars for 12 pounds.
B: 21 dollars for 12 pounds.
3 Compare
20 dollars is less than 21 dollars.
For the same 12 pounds, deal A costs less.
So deal A is the better buy.
Let's look back.
First: write both as fractions.
Then: make the same amount.
Last: compare.