The cost of a mixture of raisins and almonds is $6.60 per pound. If the ratio of raisins to almonds by weight is and the per-pound cost of almonds is twice that of raisins, what is the per-pound cost of raisins?
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Got $3.60 after setting up 5x + 3(2x) = 8(6.60). Felt pretty clean once I saw the ratio trick.
Nice, that's the same setup I used. The 8 total parts made the division easy.
Is there a way to backsolve this? I tried plugging in B but got confused with the almonds being double.
Yeah, if raisins are r, almonds are 2r. Just test the choices and see which weighted average hits 6.60.
Backsolving works but the algebra is faster here, only took me like 40 seconds.
This one tripped me up because I kept thinking the ratio gave actual weights. Took me a minute to realize you just use the parts in the weighted average.
Slightly above my comfort zone but the double-price relationship is the key. Without that it's impossible to solve.
Agreed, the 2x detail is doing all the work here. Miss it and you're stuck.
What it tests
Your ability to reason about weighted averages and the composition of mixtures.
Common trap
Averaging the percentages of two solutions without weighting by their volumes.