3 pencils cost $.03 more than 2 pen,and 1 pen

and 10 pencils together cost $2.40.Determine the
cost of each writing tool

Set up system of equations as:

Let c=pencil, p=pen, and work in cents
3c-2p=3
10c+p=240
Solve for p and c (both have to be integers).

Pen is 1.17

Pencils is 1.23

To determine the cost of each writing tool, let's assign variables to represent the costs of pencils and pens.

Let's say the cost of a pen is P dollars, and the cost of a pencil is C dollars.

According to the information given, we can now set up two equations:

Equation 1: 3P = 2C + C + 0.03
This equation states that three pencils cost $0.03 more than two pens, a pen, and the additional $0.03.

Equation 2: 10C = 2.40
This equation states that 10 pencils together cost $2.40.

Now, let's solve these equations to find the values of P and C.

From Equation 1, we can simplify it by combining like terms:
3P = 3C + 0.03

Next, we'll rearrange Equation 1 to isolate C:
3P - 3C = 0.03

Now, we divide both sides of the equation by 3:
P - C = 0.01

So, we have our first equation simplified to P - C = 0.01.

To find the value of P, we'll need another equation. Let's substitute C in terms of P from Equation 2.

Substituting C as P - 0.01 in Equation 2, we get:
10(P - 0.01) = 2.40

Next, let's distribute 10 to P and -0.01:
10P - 0.10 = 2.40

Now, let's isolate P by adding 0.10 to both sides:
10P = 2.40 + 0.10

Combining like terms:
10P = 2.50

Finally, divide both sides of the equation by 10 to solve for P:
P = 2.50 / 10
P = 0.25

Therefore, the cost of a pen is $0.25.

To find the cost of a pencil, substitute the value of P into Equation 1:
3(0.25) = 2C + C + 0.03

1.5 = 3C + 0.03

Rearrange the equation and combine like terms:
3C = 1.5 - 0.03
3C = 1.47

Divide both sides of the equation by 3:
C = 1.47 / 3
C = 0.49

Therefore, the cost of a pencil is $0.49.

So, the cost of each writing tool is:
- Pen: $0.25
- Pencil: $0.49