Calvin mixes candy that sells for $2.00 per pound with candy that costs $3.60 per pound to make 50 pounds of cancdy selling for $2.16 per pound. How many pounds of each kind of candy did he use in the mix?
I cannot figure out the other equation.
2x+3.60y=50
Please explain
To solve this problem, we need to set up a system of equations using the given information.
Let's say the amount of candy that sells for $2.00 per pound is represented by x pounds, and the amount of candy that costs $3.60 per pound is represented by y pounds.
1. The first equation is based on the total weight of the candy: x + y = 50
2. The second equation is based on the total cost of the candy: (2.00 * x) + (3.60 * y) = 2.16 * 50
Now, let's solve this system of equations:
1. x + y = 50
To isolate one variable, let's solve for y:
y = 50 - x
2. (2.00 * x) + (3.60 * y) = 2.16 * 50
Substitute the value of y from the first equation into the second equation:
(2.00 * x) + (3.60 * (50 - x)) = 2.16 * 50
Now, simplify and solve for x:
2.00x + 180 - 3.60x = 108
-1.60x = -72
x = -72 / -1.60
x = 45
Now, substitute the value of x back into the first equation to find y:
y = 50 - x
y = 50 - 45
y = 5
So, Calvin used 45 pounds of candy that sells for $2.00 per pound and 5 pounds of candy that costs $3.60 per pound to make a total of 50 pounds of candy selling for $2.16 per pound.
To solve this problem, we need to set up a system of equations. Let's call the number of pounds of candy that sells for $2.00 per pound as 'x' and the number of pounds of candy that costs $3.60 per pound as 'y'.
According to the problem statement, Calvin mixes 50 pounds of candy. This gives us our first equation:
x + y = 50
Next, we need to consider the cost of the candy mix. The total cost of the candy mix is the sum of the individual costs of each type of candy. The candy that sells for $2.00 per pound has a cost of $2.00 times the number of pounds (2x), while the candy that costs $3.60 per pound has a cost of $3.60 times the number of pounds (3.60y). The total cost is given as $2.16 per pound for 50 pounds, which gives us our second equation:
(2x + 3.60y) / 50 = 2.16
Now, we can simplify the second equation by multiplying both sides by 50 to get rid of the denominator:
2x + 3.60y = 2.16 * 50
This simplifies to:
2x + 3.60y = 108
So, our system of equations is:
x + y = 50
2x + 3.60y = 108
Now, we can solve this system of equations to find the values of x and y. One possible method to solve this system is by substitution or elimination.
Let's use the elimination method. Multiply the first equation by 2 to make the coefficients of x in both equations equal:
2(x + y) = 2(50)
2x + 2y = 100
Next, subtract this new equation from the second equation to eliminate the x variable:
(2x + 3.60y) - (2x + 2y) = 108 - 100
3.60y - 2y = 8
1.60y = 8
y = 8 / 1.60
y = 5
Now, substitute the value of y back into the first equation to solve for x:
x + 5 = 50
x = 50 - 5
x = 45
Therefore, Calvin used 45 pounds of candy that sells for $2.00 per pound and 5 pounds of candy that costs $3.60 per pound in the mix.