A box contains two different types of candy, weighs 10 pounds, and costs $14.55. One type of candy costs $1.50 a pound. The other costs $1.35 a pound. How many pounds of each kind are there?
Let's assume that the weight of the candy that costs $1.50 per pound is represented by variable x, and the weight of the candy that costs $1.35 per pound is represented by variable y.
According to the information given, the total weight of the candy is 10 pounds. So, we have the equation:
x + y = 10 --------------- Equation 1
The cost of the candy is $14.55. Since one type of candy costs $1.50 per pound and the other costs $1.35 per pound, we can set up another equation for the cost:
1.50x + 1.35y = 14.55 --------------- Equation 2
Now we can solve these two equations simultaneously to find the values of x and y.
First, let's solve Equation 1 for x:
x = 10 - y
Substitute this value of x into Equation 2:
1.50(10 - y) + 1.35y = 14.55
15 - 1.50y + 1.35y = 14.55
-0.15y = 14.55 - 15
-0.15y = -0.45
Divide both sides of the equation by -0.15:
y = -0.45 / -0.15
y = 3
Now substitute this value of y back into Equation 1 to find x:
x + 3 = 10
x = 10 - 3
x = 7
Therefore, there are 7 pounds of candy that cost $1.50 per pound and 3 pounds of candy that cost $1.35 per pound in the box.
To solve this problem, let's assign variables to represent the unknown quantities:
Let x be the number of pounds of candy that costs $1.50 per pound.
Let y be the number of pounds of candy that costs $1.35 per pound.
We know that the total weight of the candy in the box is 10 pounds, so we can set up the equation:
x + y = 10 (Equation 1)
We also know that the total cost of the candy is $14.55, so we can set up another equation using the cost per pound:
1.50x + 1.35y = 14.55 (Equation 2)
Now we have a system of two equations with two variables. To solve this system, we can use substitution or elimination. Let's use substitution.
From Equation 1, we can express y in terms of x:
y = 10 - x (Equation 3)
Substitute Equation 3 into Equation 2:
1.50x + 1.35(10 - x) = 14.55
Simplify the equation:
1.50x + 13.50 - 1.35x = 14.55
Combine like terms and solve for x:
0.15x + 13.50 = 14.55
0.15x = 14.55 - 13.50
0.15x = 1.05
x = 1.05 / 0.15
x = 7
Now we can substitute the value of x back into Equation 1 to find y:
7 + y = 10
y = 10 - 7
y = 3
Therefore, there are 7 pounds of the candy that costs $1.50 per pound and 3 pounds of the candy that costs $1.35 per pound.