Question

Gerain and Deon are making trail mix. Gerain's recipe calls for 3 parts raisins to 2 parts almonds. Dean's recipe calls for 4 parts raisins to 3 parts almonds. Which recipe has a higher concentrations of almonds?

Answer 1

To figure out which part has the higher concentration of almonds, we want to see how many almonds are there for every part in each recipe. For the first recpe, we have 2 parts almond for ever 5 total parts, and in the second part, we have 3 parts almonds for every 7 total parts, so we can represent them as the fractions:

$\text{Gerain's concentration}: \frac{2}{5}\\ \text{Deon's concentration}: \frac{3}{7}$

So, which one is greater? Well, let's say they both make 35 total batches (36 is the least commun multiple of the two denominators) that would give them:

$\frac{2}{5}*35=2*7=14\text{ parts raisins}\\ \frac{3}{7}*35=3*5=15 \text{ parts raisins}$

So we have Deon's recipe as the large concentration of raisins.