Final answer:
Each apple costs $0.75, which is determined by setting up a system of linear equations from the given information and solving for the cost of an apple.
Step-by-step explanation:
In order to determine the cost of each apple when Ian buys 3 pears and 4 apples for $4.50, and the total cost of one apple and one pear is $1.25, we can set up a system of equations to solve for the individual prices of an apple and a pear. Let's denote the cost of an apple as 'A' and the cost of a pear as 'P'.
The information given translates into the following equations:
This is a system of linear equations that can be solved using substitution or elimination methods. A common approach is to solve the second equation for one variable and substitute it into the first.
Let's solve for 'P' from the second equation: P = $1.25 - A. Substituting 'P' in the first equation gives: 3($1.25 - A) + 4A = $4.50. Simplifying this we get: $3.75 - 3A + 4A = $4.50, which simplifies to A = 75 cents.
Therefore, each apple costs $0.75.