You need a 100 pounds of two types of candy that cost 50 cents per pound and 75 cents per pound.

A.) Verify that your total cost is c(x)=0.50x + 0.75(100-x)

thx a ton:)

To verify that the total cost formula c(x) = 0.50x + 0.75(100-x) is correct, we need to understand what each term in the formula represents.

In this scenario, you want to buy a total of 100 pounds of two types of candy that cost 50 cents per pound and 75 cents per pound.

Let's break down the formula:

1. The term 0.50x represents the cost of the first type of candy, which costs 50 cents per pound. Here, 'x' represents the number of pounds of the first type of candy.

2. The term 0.75(100-x) represents the cost of the second type of candy, which costs 75 cents per pound. Here, '100-x' represents the number of pounds of the second type of candy. Since you want a total of 100 pounds of candy, the remaining weight after selecting 'x' pounds of the first type is 100-x pounds.

3. Finally, adding both terms in the formula, 0.50x and 0.75(100-x), gives you the total cost of purchasing the two types of candy.

To verify whether the formula is correct, you can substitute different values for 'x' and evaluate the expression on both sides of the equation. If the expressions are equal for all values of 'x', then the formula c(x) = 0.50x + 0.75(100-x) is valid.

For example, assuming you want to buy 30 pounds of the first type and 70 pounds of the second type, you would substitute 'x = 30' into the formula:

c(30) = 0.50(30) + 0.75(100-30)
c(30) = 15 + 0.75(70)
c(30) = 15 + 52.5
c(30) = 67.5

So, the total cost of buying 30 pounds of the first type of candy and 70 pounds of the second type is $67.50.

You can perform similar calculations for other values of 'x' to further verify the formula.