A natural food store makes its own brand of trail mix out of dried apples, raisins, and peanuts. One pound of the mixture costs 3.18. It contains twice as much peanuts by weight as apples. One pound of dried apples cost $4.48, a pound of raisins costs $2.40, and a pound of peanuts cost $3.44. This is a three variable system. I represented x=apples, y=raisins, z=peanuts.
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To represent the given information in a three-variable system, we can assign variables to each ingredient as follows:
- Let x represent the weight of dried apples in pounds.
- Let y represent the weight of raisins in pounds.
- Let z represent the weight of peanuts in pounds.
Based on the given information, we know the following relationships:
1. The cost of one pound of the mixture is $3.18.
2. The weight of peanuts is twice the weight of dried apples.
3. The cost of each ingredient per pound is given: $4.48 for dried apples, $2.40 for raisins, and $3.44 for peanuts.
With this information, we can create the following equations:
1. Cost equation:
The cost of one pound of the trail mix is the sum of the individual ingredient costs:
3.18 = 4.48 * x + 2.40 * y + 3.44 * z
2. Weight equation:
The weight of peanuts is twice the weight of dried apples:
z = 2 * x
Now, we have two equations with three variables. To solve the system, we need to use substitution or elimination.
Let's use substitution:
- Substitute the value of z from the second equation into the first equation:
3.18 = 4.48 * x + 2.40 * y + 3.44 * (2 * x)
3.18 = 4.48 * x + 2.40 * y + 6.88 * x
3.18 = 11.36 * x + 2.40 * y
Now, we have one equation with two variables. To solve for either x or y, we need one more equation.
Assuming we have another piece of information or equation, we can find the values of x, y, and z by solving the system of equations. However, with the given information, we cannot determine the exact weights of apples, raisins, and peanuts.