Question

Suppose you want to fill nine 1-lb tins with a snack mix. You have 15 and plan to buy almonds for 2.45 per lb , hazelnuts for 1.85 per lb , and raisins for .80 per lb . You want the mix to contain an equal amount of almonds and hazelnuts and twice as much of the nuts as the raisins by weight.

c. How many of each ingredient should you buy?

Answer 1

To determine how many of each ingredient to buy, we can set up a system of equations. Solving the system, we find that you should buy 0 pounds of almonds and hazelnuts, and 9 pounds of raisins.

Step-by-step explanation:

To determine how many of each ingredient you should buy, let's set up a system of equations. Let's say you need x pounds of almonds, y pounds of hazelnuts, and z pounds of raisins. According to the problem, you want the mix to contain an equal amount of almonds and hazelnuts, so x = y. You also want the nuts to be twice as much as the raisins, so x + y = 2z. Lastly, you want to fill nine 1-lb tins, so x + y + z = 9.

You now have a system of three equations with three variables:

x = y

x + y = 2z

x + y + z = 9

Since x = y, we can substitute y with x in the second and third equations:

x + x = 2z

2x + z = 9

We can solve this system of equations:

Subtracting the first equation from the second equation, we get:

2x + z - (x + x) = 9

2x + z - 2x = 9

z = 9

Substituting z = 9 back into the second equation, we get:

2x + 9 = 9

2x = 0

x = 0

Since x = y, y = 0 as well.

So, you should buy 0 pounds of almonds and 0 pounds of hazelnuts. However, since you want the mix to contain nuts, you should buy some raisins. Since the ratio of nuts to raisins is 2:1, you can buy 9 pounds of raisins.

Answer 2

To fill the snack mix tins as per the given ratios, the student should buy 3 lbs each of almonds, hazelnuts, and raisins, resulting in a total of 9 lbs to fill nine 1-lb tins.

Step-by-step explanation:

The student wants to fill nine 1-lb tins with a snack mix, containing an equal amount of almonds and hazelnuts, and twice as much of the nuts (combined weight) as raisins by weight. To find out how many of each ingredient to buy, we need to calculate the weights for each, based on the given ratios and total weight required.

To do that, let's denote the weight of raisins as R lbs. Because the amount of nuts is twice as much as raisins, we know that (almonds + hazelnuts) will be 2R lbs. Since almonds and hazelnuts are to be in equal amounts, we will have R lbs of almonds and R lbs of hazelnuts. The tins must contain in total 9 lbs (9 tins x 1 lb/tin), which equals R + 2R = 3R. Therefore, R must equal 3 lbs, since 3R = 9.

This means the student should buy 3 lbs of raisins, and twice that amount for the nuts, which is 6 lbs of nuts in total, or 3 lbs of almonds and 3 lbs of hazelnuts. That's:

• 
  
• 3 lbs of almonds
• 
  
• 3 lbs of hazelnuts
• 
  
• 3 lbs of raisins