Question

One ounce of raisins by weight sells for 22 cents and one ounce of bran flakes by weight sells for 12 cents. How many ounces of each should be used to create a 20 ounce box of raisin bran cereal that can be sold for 15 cents an ounce?

Answer 1

We need 6 ounces of raisins and 14 ounces of bran flakes to create a 20-ounce box of raisin bran cereal that sells for 15 cents an ounce.

Step-by-step explanation:

To find out how many ounces of raisins and bran flakes should be used in a 20 ounce box of raisin bran cereal that sells for 15 cents an ounce, we can set up two equations based on the given price and weight information. Let x be the number of ounces of raisins and y be the number of ounces of bran flakes. We have two conditions to meet:

• The total weight of the mix should be 20 ounces, so x + y = 20.
• The total cost of the mix should be 15 cents per ounce for a 20-ounce mix, so 0.22x + 0.12y = 15 * 20, which simplifies to 0.22x + 0.12y = 3 (since 15 cents multiplied by 20 ounces equals $3).

Now we solve the system of equations:

1. From x + y = 20, we extract y = 20 - x.
2. We substitute the value of y in the second equation to get 0.22x + 0.12(20 - x) = 3.
3. We simplify the equation to get 0.22x + 2.4 - 0.12x = 3, and then 0.10x = 0.6.
4. Dividing both sides of the equation by 0.10 gives us x = 6. Thus, we need 6 ounces of raisins.
5. Substituting x = 6 into y = 20 - x, we find that y = 14. So, we need 14 ounces of bran flakes.

To summarize, to create a 20-ounce box of raisin bran cereal, we need 6 ounces of raisins and 14 ounces of bran flakes.