Final answer:
The store used 4 lbs of oatmeal, 2 lbs of crispies, and 5 lbs of chocolate chips for the 11-lb mixture, based on the cost and weight restrictions provided in the question.
Step-by-step explanation:
The student is asking to solve a system of equations based on the cost and weight of a mixture of ingredients. To find out how much of each ingredient the store used, we can set up equations based on the given prices and total weight and cost.
Let's denote the weight of oatmeal as O, the weight of crispies as C, and the weight of chocolate chips as Ch. We know the following:
- Total weight is 11 lbs, so O + C + Ch = 11
- Oatmeal costs $1.50/lb and the mixture calls for twice as much oatmeal as crispies, so O = 2C
- The total cost of the mixture is $17.00
Now we create an equation representing the total cost: 1.50O + 2.00C + 1.00Ch = $17.00. We already know that O can be substituted with 2C, so the new cost equation becomes 1.50(2C) + 2.00C + 1.00Ch = 17 or 3C + 2C + Ch = 17. Now simplifying we get:
5C + Ch = 17
Since we have two equations (O + C + Ch = 11 and 5C + Ch = 17) and we know that O = 2C, we can solve for C and Ch.
Substituting O with 2C in the weight equation, we get 2C + C + Ch = 11, which simplifies to 3C + Ch = 11. Combining both the cost and weight equations, we can solve for C and Ch and then use O = 2C to find O. Solving these gives us the amounts of each ingredient as follows: Oatmeal: 4 lbs, Crispies: 2 lbs, Chocolate Chips: 5 lbs.