Thread: 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?

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:



But we still need another relation. Let's go back to the table. We can see that the total weight is expressed as:



But what is c and d?

Remember, they gave you the price/weight for dried fruits:




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.

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 = number of kilograms of fruit.
. . At $3.75/kg, its total value is: . dollars.
Write that into the first row of our chart.





Then = number of kilograms of granola.
. . At $1.75/kg, its total value is: . dollars.
Write that in the second row of our chart.





The final mixture is 30 kg of mix worth $2.75/kg.
. . Its total value is: .
Write that in the third row of our chart.





The third column gives us our equation:

. .


Therefore, we have: .