1. ## mixture question

Conrad works at a bulk-food store. His manager asks him to mix some
dried fruit (that cost $3.75/kg) with some granola (that costs$1.75/kg) to
make 30 kg of trail mix that will sell for $2.75/kg. How many kilograms of dried fruit are in the trail mix? 2. I drew this table to make things clearer for you. The total price is found by multiplying the Price/Weight by Weight. Now, let's analyze the table. We can see that the total price is expressed as:$\displaystyle a + b = 82.5$But we still need another relation. Let's go back to the table. We can see that the total weight is expressed as:$\displaystyle c + d = 30$But what is c and d? Remember, they gave you the price/weight for dried fruits:$\displaystyle \frac{a}{c} = 3.75\displaystyle \frac{b}{d} = 1.75$Can you work your way from here? Hint: Try to write the total weight expression in terms of a and b. Then it only becomes a matter of simple substitution. 3. Hello, euclid2! Conrad works at a bulk-food store. His manager asks him to mix some dried fruit that cost$3.75/kg
with some granola that costs $1.75/kg to make 30 kg of trail mix that will sell for$2.75/kg.
How many kilograms of dried fruit are in the trail mix?

Let $\displaystyle x$ = number of kilograms of fruit.
. . At $3.75/kg, its total value is: .$\displaystyle 3.75x$dollars. Write that into the first row of our chart.$\displaystyle \begin{array}{c|c|c|c|}
& & \text{Unit} & \text{Total} \\
& \text{kg.} & \text{price} & \text{value} \\ \hline
\text{Fruit} & x & \$3.75 & 3.75x \\ \text{Granola} & & & \\ \hline \text{Mixture} & & & \end{array}$

Then $\displaystyle (30-x)$ = number of kilograms of granola.
. . At $1.75/kg, its total value is: .$\displaystyle 1.75(30-x)$dollars. Write that in the second row of our chart.$\displaystyle \begin{array}{c|c|c|c|}
& & \text{Unit} & \text{Total} \\
& \text{kg.} & \text{price} & \text{value} \\ \hline
\text{Fruit} & x & \$3.75 & 3.75x \\ \text{Granola} & 30-x & \$1.75 & 1.75(30-x) \\ \hline
\text{Mixture} & & & \end{array}$The final mixture is 30 kg of mix worth$2.75/kg.
. . Its total value is: .$\displaystyle (30)(\$2.75) \:=\:\$82.50$
Write that in the third row of our chart.

$\displaystyle \begin{array}{c|c|c|c|} & & \text{Unit} & \text{Total} \\ & \text{kg.} & \text{price} & \text{value} \\ \hline \text{Fruit} & x & \$3.75 & 3.75x \\
\text{Granola} & 30-x & \$1.75 & 1.75(30-x) \\ \hline \text{Mixture} & 30 & \$2.75 & 82.50 \end{array}$The third column gives us our equation: . .$\displaystyle \text{(Total Value of Fruit) } + \text{ (Total Value of Granola)} \;=\;\text{(Total Value of Mixture)}$Therefore, we have: .$\displaystyle {\color{blue}3.75x + 1.75(30-x) \;=\;82.50}\$