A grocer wants to mix two kinds of candy. One kind sells for 2.75 per pound and the other sells for 2.95 per pound. He wants to mix a total of 17 pounds and sell it for 2.85 per pound. How many pounds of each kind should he use in the new mix?

Question

anonymous · Answer

didn't I answer this already? his target price is halfway between the two, so he should mix half and half.

anonymous · Answer

You need to write 2 sets of linear equations and solve them by substitution, elimination or what method you fancy.

Let the 2.75 per pound candy be "x" pounds and let the 2.95 candy be "y" pounds.
If you add "x" and "y" you'll get 17 pounds altogether.  Write that as an equation.
Now you also need an equation for the cost of the candy.  The cost of the candy is the amount of pounds multiplied by the cost per pound.  If Mr Grocerman adds the cost of "x" times 2.75 dollars per pound to the cost of "y" times 2.95 dollars per pound it will add to 17 times the target 2.85 dollars per pound.  There's your other equation.  Now solve for one variable and substitute into the first equation to find the other variable.

anonymous · Answer

I think my way is easier, in this case. you will have to use this other method in the general case where you can't just see the answer.

anonymous · Answer

I think your way is easier too.  Some horrid teacher might want an algebraic explanation with work though.