Answer:
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.