Question

A store sells a mixture of peanuts and raisins for $1.75 per pound. If peanuts cost $1.25 per pounds and raisins cost $2.75 per pound, what amount of raisins and peanuts go into 1 pound of the mixture?

Answer 1

To find the amount of raisins and peanuts in 1 pound of the mixture, set up a system of equations based on the given information. Solve the system using the elimination method to find that 2/3 pound of peanuts and 1/3 pound of raisins go into 1 pound of the mixture.

Step-by-step explanation:

To find the amount of raisins and peanuts in 1 pound of the mixture, we need to set up a system of equations based on the given information.

Let's assume x represents the amount of peanuts in pounds and y represents the amount of raisins in pounds.

We know that the cost per pound of the mixture is $1.75, so we can write the equation: 1.25x + 2.75y = 1.75.

We also know that the total weight of the mixture is 1 pound, so we can write the equation: x + y = 1.

To solve this system of equations, we can use a method such as substitution or elimination. In this case, let's use the elimination method.

Multiplying the second equation by 2.75, we get 2.75x + 2.75y = 2.75.

Subtracting this equation from the first equation, we eliminate y and solve for x:

1.25x - 2.75x = 1.75 - 2.75

-1.5x = -1

Dividing both sides of the equation by -1.5, we find that x = 2/3.

Now, we can substitute this value of x back into the second equation to solve for y:

(2/3) + y = 1

y = 1 - 2/3

y = 1/3

Therefore, 2/3 pound of peanuts and 1/3 pound of raisins go into 1 pound of the mixture.

Answer 2

1/2 pound
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