Question

A box of candy containing two different types, weighs 10 pounds, and costs $14.55. One type of candy costs $1.50 a pound. The other type costs $1.35 a pound. How many pounds of each kind are there?

Answer 1

Let x equal the kind of candy that costs $1.50 a pound
Let y equal the kind of candy that costs $1.35 a pound
We're going to need to make a system of equations, or two equations with the same variables.
x + y = 10
1.5x + 1.35y =14.55
Now, we're going to take the first equation and isolate a variable
x = 10-y
Next, we replace the x in the second equation with our new expression for x
1.5(10-y) + 1.35y = 14.55
Solve for Y
15 - 1.5y +1.35y = 14.55
15 - 0.15y = 14.55
-0.15y = -0.45
y=3
Then, take the y value and plug it into either equation. We're going to use the first one because it's easier.
x + y = 10
x + 3 = 10
x = 7
Finally, plug your two numbers into the second equation to check.
1.5x + 1.35y =14.55
1.5(7) + 1.35(3) = 14.55
10.50 + 4.05 = 14.55
14.55 = 14.55