Question

How much candy at 1.16 dollars a pound should be mixed with candy worth 86 cents a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound?
(a) 28 pound of 1.16 dollars and 32 pounds of 86 cents
(b) 32 pound of 1.16 dollars and 28 pounds of 86 cents
(c) 40 pound of 1.16 dollars and 12 pounds of 86 cents
(d) None of these

Answer 1

Hint: To start with, we are to find the amount of candies needed with the given conditions to get our desired result. Now, we will try to solve it by considering x pounds of 1.16 dollar candy and y pounds of 86 cents. Then by the given conditions we can form two equations involving x and y. Solving the equations will give us our needed result.

Complete step by step answer:
According to the question, we are to find how much candy at 1.16 dollars a pound should be mixed with candy worth 86 cents a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound.
So, to start with, we have two types of candy. Let x be the candy costing 1.16 dollars a pound. Let y be the candy costing 0.86 dollars per pound.
We want to end up with 60 pounds of candy so we get the equation that, x + y = 60.
We also know that we want the average cost to be 1 dollar per pound. To get the average cost we need to know the total cost and divide by the total pounds.
Now, the total cost: 1.16x + 0.86y and the total pounds: 60
Our needed cost per pound: 1 dollar
So, we get our equation as, $\dfrac{1.16x\text{ }+\text{ }0.86y}{60}=1$ ,
Multiply both sides with 60, we get, 1.16x + 0.86y = 60, which is the second equation.
Now, multiplying the first equation by -0.86 to get: -0.86 x -0.86 y= - 51.6
Adding the second equation with this one, the term y is cancelling out.
Thus, we are getting, 0.3x = 8.4
Again, dividing both sides through by 0.3, we are having,
$x=\dfrac{8.4}{0.3}=28$
Putting the value in the first equation, we get, 28 + y = 60.
Then, we have the value of y as, y = 32.
So, we want 28 pounds of the candy costing 1.16 dollars and 32 pounds of the candy costing 0.86 dollars.

Hence, the solution is, (a) 28 pound of 1.16 dollars and 32 pounds of 86 cents.

Note:
After getting two equations, we can solve the equations using different types of ways. Here we have used the rule of equating coefficients, whereas they can be solved using the substitution method. That can be done by finding the value of x from the first equation and putting the value in the other equation to eliminate x and find the value of y. Similarly the value of x can be found.