# How many pounds of dried pineapple selling at 35 cents a pound should be mixed with dried apricots selling at 70 cents a pound to make a mixture of 100 pounds to sell at 42 cents per pound?

Aug 9, 2015

You need 80 lbs of dried pineapple and 20 lbs of dried apricots.

#### Explanation:

In order to solve this problem, you need to use the information given to write two equations, one that relates the masses of the two types of dried fruit and the other that relates the profit you would get for the two types of dried fruit and for the mixture.

Let's say that $x$ represents the mass of dried pineapple and $y$ represents the mass of dried apricots. The final mass of the mixture is 100 lbs, which means that you can write

$x + y = 100$

Now focus on the profit. You know that the mixture can be sold for $0.42 per pound, the dried pineapple for $0.35 per pound, and the dried apricots for $0.70 per pound. This means that you can write ${\underbrace{x \cdot 0.35}}_{\textcolor{b l u e}{\text{profit for x")) + underbrace(y * 0.70)_(color(green)("profit for y")) = underbrace(100 * 0.42)_(color(orange)("profit for mix}}}$The system of equations looks like this $\left\{\begin{matrix}x + y = 100 \\ 0.35 x + 0.70 y = 42\end{matrix}\right.$Use the fist equation to write $x$as a function of $y$, then the second equation to find $y$$x = 100 - y$$0.35 \cdot \left(100 - y\right) + 0.70 y = 42$$35 - 0.35 y + 0.70 y = 42$$0.35 y = 7 \implies y = \frac{7}{0.35} = \textcolor{g r e e n}{20}$This means that $x$is equal to $x = 100 - 20 = \textcolor{g r e e n}{80}$Therefore, you need to mix 80 lbs of dried pineapple at $0.35 per pound with 20 lbs of dried apricots at $0.70 per pound to get a mixture that can be sold for $0.42 per pound.