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.

e) none of the above because the measure of angle cba is 101°

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)