Question

Four pens and three pencils cost $\$2.24$. Two pens and five pencils cost $\$1.54$. No prices include tax. In cents, what is the cost of a pencil?

Answer 1

Let's start by defining some variables to help us solve the problem:
- Let p be the price of a pen in cents.
- Let c be the price of a pencil in cents.

From the first sentence of the problem, we can write the following equation based on the cost of four pens and three pencils:
4p + 3c = 224 ... (Equation 1)

From the second sentence of the problem, we can write the following equation based on the cost of two pens and five pencils:
2p + 5c = 154 ... (Equation 2)

We now have two equations and two variables, which we can solve using algebra. We can start by multiplying Equation 2 by 2 to eliminate p and obtain:
4p + 10c = 308 ... (Equation 3)

We can now subtract Equation 1 from Equation 3 to eliminate 4p and obtain:
7c = 84

Solving for c, we get:
c = 12

Therefore, the cost of a pencil is 12 cents.