i need to know exactly the formula of how to do these types of problems because i have spend seriously over an hour trying to do this one problem. HELP!
A dealer mixes candy worth 90 cents per pound with candy worth 65 cents per pound in order to obtain 40 pounds of candy to be sold at 75 cents per pound. how many pounds of the 90 cent candy should be used?
There is no "formula" to solve these kind of problems, you basically have to translate the English into a mathematical statement.
let the number of pounds of the 90 cent candy be x
then the amount of 65 cent candy is 40-x pounds.
so....
90x + 65(40-x) = 75(40)
Now just solve that equation.
To solve this problem, we can use a basic equation relating the quantities and values of the two types of candy. Let's break down the problem step by step.
1. Define the variables:
Let's call the amount of candy worth 90 cents per pound as "x" (in pounds).
2. Set up the equation:
The total weight of the candy is given as 40 pounds. So, the weight of the candy worth 65 cents per pound is (40 - x) pounds.
Using the values, the equation becomes:
90x + 65(40 - x) = 75 * 40
3. Solve the equation:
Now, you can solve this equation for x to find the amount of candy worth 90 cents per pound.
First, distribute the 65 to the terms inside the parentheses:
90x + 65 * 40 - 65x = 75 * 40
Next, simplify the equation:
90x + 2,600 - 65x = 3,000
Combine like terms:
25x + 2,600 = 3,000
Subtract 2,600 from both sides:
25x = 400
Divide both sides by 25:
x = 16
Therefore, you should use 16 pounds of the candy worth 90 cents per pound.
Remember to check your answer! You can plug the value of "x" back into the original equation to ensure it satisfies the equation.
Hope this explanation helps, and don't hesitate to ask if you have any more questions!