A candy store makes a 10-lb mixture of gummy worms, candy corn, and sourballs. The cost of gummy worms is $1.00 per pound, candy corn cost $3.00 per pound, and sourballs cost $1.50 per pound. The mixture calls for three times as many gummy worms as candy corn. The total cost of the mixture is $15.00. How much of each ingredient did the store use?

6 grams of gummy worms, 2 grams of candy corn and 2 grams of sourballs.

Step-by-step explanation:

Let the number of pounds of each ingredient be as follows:

Gummy Worms = x pounds

Candy Corn = y pounds

Sourballs = z pounds

The store makes a mixtures of 10 pounds. This means the sum of x, y and z would be 10. Setting up the equation:

                                    (Equation 1)

The mixture calls for 3 times as many gummy worms as candy corn. This means amount of gummy worm will be 3 times the candy corn. Setting up the Equation:

                                                 (Equation 2)

Cost of gummy worms is $1.00 per pound, candy corn cost $3.00 per pound, and sourballs cost $1.50 per pound. So cost of x, y and z pounds would be:

1x , 3y and 1.5z, respectively. The total cost of mixture is $15. So we can set up the Equation as:

                               (Equation 3)

Using the value of x from Equation 2, in Equations 1 and 3 give us following two equations:

                            By substitution in Equation 1. (Equation 4)                        By substitution in Equation 3. (Equation 5)

Multiplying the Equation 4 by 1.5 and subtracting from Equation 5 gives us:

When two sides of equations turn into something that is always positive, we conclude that there are infinite number of solutions. In such cases, we fix a variable and give different values to it, to find corresponding values of other variables. Lets re-write the solution in terms of z.

From Equation 4, we have:

From Equation 2, we have:

Therefore, the solution set will be:

Now in order to find any combination of ingredient, we give any value to z. Let, z is equal to 2 grams.

So,

x would be = 6 grams

y would be = 2 grams

So, one of the possible amount of ingredients that store can use is:

6 grams of gummy worms, 2 grams of candy corn and 2 grams of sourballs.

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i