Question

A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?

Answer 1

You need a table for this, and I will gladly assist you in figuring this out!The thing with this is, you need to fill in as much of the table as you can using the info you have. The first piece of info you have is that the total amount of mix the grocer wants to make is 10 lbs. That number goes into you peanut/cashew mix row under the "amount nuts" column. The you have that he wants that mix to cost $4.75 a pound. That number goes into the same row, but in the column marker "price per pound" (the middle column). You know that peanuts cost $4 a pound, so that goes into the peanut row in the price per pound column, and that cashews cost 6.50 a pound, so that number goes into the cashew row in the price per pound column. Now you only have to decide what numbers go into the first column in the peanut and the cashew rows. Well, if the grocer wants a total of 10 pounds, and we don't know how much of either he needs, if we call peanuts "x", then what would cashews have to be? 10-x, right? So fill that in. The last column is what I call the answers column; it is the one we will use to set up an equation and solve the problem. Let's draw it again, with all the values this time, and see what's what. To get the last column filled in, you simply multiply each row straight across and enter the answer in that box. x * 4 = 4x in the first box in the last column. (10-x)6.50 requires you to do some distributing of the $6.50 into the parenthesis. You do that and get 65 - 6.50x. And the last box is just multiplying 10 * 4.75 to get 47.5. Now we take the first two boxes in the last column and add them together and set them equal to the last box in that column because we are, after all, adding the mixes together to get a final mix of some of both. We just need to figure out how much of each, and that's what solving for x will tell you. So your equation is
4x + 65 - 6.50x = 47.5. Combine your x terms to get -2.5x + 65 = 47.5. Now subtract 65 from both sides to get -17.5. Now we have -2.5x = -17.5. Solve for x! x = 7. So this means, according to our chart we made, that we need 7 pounds of peanuts and 10-7 pounds of cashews, or 3 pounds. See that?