Problema Solution
Sue owns a candy store, and she wants to mix gummy worms worth $3 per pound with gummy bears worth $1.50 per pound to make 30 pounds of a mixture worth $63.00
Analyze and set up a system of equations for this mixture.
Solve this system of equations to determine how many pounds of each candy Sue should use for this mixture.
Answer provided by our tutors
Start off by setting up the system of equations. The problem tells us that she is selling gummy worms at $3 per pound, so we can signify that with 3x. Gummy bears are being sold at $1.50 per pound, which we can signify with 1.50y. Both of those figures added together will total to $63.00, so our first equation will look as follows:
3x + 1.50y = 63.00
For our 2nd equation, we can use the fact that the some of the candy weights adds up to 30 pounds. We represented the weights in the other equation with "x" and "y", so the 2nd equation will be as follows:
x + y = 30
So now that we have both equations, we can start solving the system.
3x + 1.50y = 63.00
x + y = 30
There are various ways that you can solve it, but I will use substitution. First, solve for x in your 2nd equation:
x = 30 - y
Then plug that into your first equation and solve for y:
3(30 - y) + 1.50y = 63.00
90 - 3y + 1.50 = 63.00
-1.5y = -27
y = 18 pounds of gummy bears
Now just simply plug that value of y back into the 2nd equation and solve for x:
x + 18 = 30
x = 12 pounds of gummy worms