Pail has just enough money to buy 5 erasers and 30 pencils or 10 erasers and 24 pencil. Each eraser costs 30 cents. How much does each pencil cost?
Write an algebraic equation to solve for the pencil cost (x).
5(0.3)+30x= 10(0.3) + 24x
1.50 +30x=3+24x
1.50+6x=3
6x=1.5
x=1.5/6=0.25
The cost of the pencil is $0.25.
Let's assume the cost of each pencil is x cents.
From the given information, we can set up the following equations:
5 erasers + 30 pencils = Pail's money
or
5 * (30 cents) + 30 * x = Pail's money
10 erasers + 24 pencils = Pail's money
or
10 * (30 cents) + 24 * x = Pail's money
Since the two equations represent the same amount of money, we can set them equal to each other:
5 * (30 cents) + 30 * x = 10 * (30 cents) + 24 * x
By simplifying and solving for x, we can determine the cost of each pencil.
To find the cost of each pencil, we can set up a system of equations based on the provided information.
Let's assume the cost of each pencil is x cents.
According to the given information:
Pail can buy 5 erasers and 30 pencils with his available money. This can be written as:
5 * 30 + 30 * x = P (where P represents the amount of money Pail has)
Similarly, Pail can also buy 10 erasers and 24 pencils with the same amount of money. This equation can be written as:
10 * 30 + 24 * x = P
Now, let's solve these two equations to find the value of x, which represents the cost of each pencil.
From the first equation:
150 + 30x = P
From the second equation:
300 + 24x = P
Since both equations equate to the same value, we can equate them to each other:
150 + 30x = 300 + 24x
By simplifying the equation, we get:
6x = 150
Dividing both sides of the equation by 6, we find:
x = 25
Therefore, each pencil costs 25 cents.