Six pears and three apples cost $3.90$. Two pears and five apples cost $3.30$. How much does one pear cost?

Hint: In the given question, we have been asked to find the cost of 1 pear and it is given that six pears and three apples cost $3.90$, two pears and five apples cost $3.30$. According to this, we need to make two linear equations and after that we will solve the system of linear equations by the substitution method.

Complete step-by-step solution:
Let assume ‘p’ is the cost of each pear and ‘a’ is the cost of each apple.
We have given that,
Six pears and three apples cost $3.90$.
Converting it into equation, we get
\[\Rightarrow 6p+3a=3.90\]
And,
Two pears and five apples cost $3.30$.
Converting it into equation, we get
\[\Rightarrow 2p+5a=3.30\]
We get two equation,
\[\Rightarrow 6p+3a=3.90\]------ (1)
\[\Rightarrow 2p+5a=3.30\]------ (2)
Multiply the second equation by 3, we get
\[\Rightarrow 6p+15a=9.90\]
Now solving for the value of 6p, we get
\[\Rightarrow 6p=9.90-15a\]
Now, substituting the value of \[6p=9.90-15a\] in equation (1), we get
\[\Rightarrow 9.90-15a+3a=3.90\]
Combining the like terms, we get
\[\Rightarrow 9.90-12a=3.90\]
Now, solving for the value of ‘a’, we get
\[\Rightarrow -12a=3.90-9.90\]
\[\Rightarrow -12a=-6\]
\[\Rightarrow a=0.50\]
\[\therefore \] The cost of 1 apple is $0.50.$
Now, substituting the value of \[a=0.50\] in equation (2), we get
\[\Rightarrow 2p+5\times 0.50=3.30\]
Simplifying the above equation, we get
\[\Rightarrow 2p+2.50=3.30\]
Now, solving for the value of ‘p’, we get
\[\Rightarrow 2p=3.30-2.50\]
\[\Rightarrow 2p=0.80\]
\[\Rightarrow p=0.40\]
\[\therefore \] The cost of 1 pear is $0.40$.

Thus, one pear costs $0.40$ is the required answer.

Note: Students should always write the digits very carefully as it is the most common mistake while solving linear equations and carefully taking each mathematical operation. The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.