2470.31 – Jellybean Profits

Sophia buys jellybeans wholesale: 25 cents for 100. She repackages them in bags of 30 and sells a bag for 20 cents. How many bags must she sell to realize a profit of $20.00?

Solution

It turns out one jellybean costs 14\dfrac{1}{4} of a cent and sells for 23\dfrac{2}{3} of cent. The profit per jelly bean is

23−14=8−312=512 cents.\dfrac{2}{3} - \dfrac{1}{4} = \dfrac{8 - 3}{12} = \dfrac{5}{12} \text{ cents.}

If she wants to realize $20 in profit she will need to sell xx jellybeans and

512x=2000 cents⇝x=12⋅20005=4800 jellybeans.\dfrac{5}{12} x = 2000 \text{ cents} \leadsto x = \dfrac{12 \cdot 2000}{5} = 4800 \text{ jellybeans}.

At 30 jellybeans per package, that is 480030=160 bags.\dfrac{4800}{30} = 160 \text{ bags}.

What do you suppose all of those bags of jellybeans weigh?