Question

A candy maker has $60$ $pounds$ of candy that sells for $\$1.50/\mathrm{lb}$ which is consisted of jellybeans and gumdrops.

If Jellybeans sell for $\$1.20/\mathrm{lb}$ and gumdrops sell for $\$2.00/\mathrm{lb}$, how many $pounds$ of gumdrops are there in the mixture?

Answer 1

Find the amount of pounds of gumdrops that are present in the mixture:

Let $x$ represent amount of gumdrops.

Since she has $60$ $pounds$ of candy, then the amount of jellybean is $\left(60-x\right)$.

Given that the Jellybeans sell for $\$1.20/\mathrm{lb}$ and gumdrops sell for $\$2.00/\mathrm{lb}$.

Calculate the value of $x$ as shown:

$$\begin{gathered} 1.2\left(60-x\right)+2x=1.5\left(60\right) \\ \Rightarrow 72-1.2x+2x=90 \\ \Rightarrow 72+0.8x=90 \\ \Rightarrow 0.8x=90-72\left[\mathrm{Subtracting}72\mathrm{from}\mathrm{both}\mathrm{sides}\right] \\ \Rightarrow 0.8x=18 \\ \Rightarrow x=\frac{18}{0.8}\left[\mathrm{Divide}\mathrm{each}\mathrm{side}\mathrm{by}0.8\right] \\ \therefore x=22.5 \end{gathered}$$

Therefore, $22.5$ $pounds$ of gumdrops are present in the mixture.