Welcome to the article Mr Tan had just enough money to buy 80 pens However he bought only 60 pens and had 51 left What was the cost of. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
- Let $T$ be the total money Mr. Tan had and $C$ be the cost of each pen.
- Express $T$ in two ways: $T = 80C$ and $T = 60C + 51$.
- Equate the two expressions: $80C = 60C + 51$.
- Solve for $C$: $C = \frac{51}{20} = 2.55$. The cost of each pen is $\boxed{2.55}$.
### Explanation
1. Problem Analysis
Let's analyze the problem. Mr. Tan had enough money to buy 80 pens. He bought only 60 pens and had $51 left. We need to find the cost of each pen. Let's denote the total amount of money Mr. Tan had as $T$, and the cost of each pen as $C$.
2. Expressing the Total Amount of Money
We can express the total amount of money Mr. Tan had in two ways. First, since he had enough money to buy 80 pens, we have $T = 80C$. Second, since he bought 60 pens and had $51 left, we have $T = 60C + 51$.
3. Equating the Expressions
Now we can equate the two expressions for $T$: $$80C = 60C + 51$$
4. Solving for C
Next, we solve for $C$. Subtract $60C$ from both sides:$$80C - 60C = 51$$This simplifies to:$$20C = 51$$
5. Finding the Cost of Each Pen
Finally, divide both sides by 20 to find the cost of each pen:$$C = \frac{51}{20} = 2.55$$So, the cost of each pen is $2.55.
6. Final Answer
Therefore, the cost of each pen is $2.55.
### Examples
Imagine you are planning a school event and need to buy stationery. Knowing how to calculate the cost of individual items when given a total budget and leftover money helps you manage your expenses effectively. For example, if you know you have a budget for 100 pencils but only buy 75 and have $12.50 left, you can calculate the cost of each pencil to better plan your remaining purchases. This skill is useful in budgeting and making informed purchasing decisions.
- Express $T$ in two ways: $T = 80C$ and $T = 60C + 51$.
- Equate the two expressions: $80C = 60C + 51$.
- Solve for $C$: $C = \frac{51}{20} = 2.55$. The cost of each pen is $\boxed{2.55}$.
### Explanation
1. Problem Analysis
Let's analyze the problem. Mr. Tan had enough money to buy 80 pens. He bought only 60 pens and had $51 left. We need to find the cost of each pen. Let's denote the total amount of money Mr. Tan had as $T$, and the cost of each pen as $C$.
2. Expressing the Total Amount of Money
We can express the total amount of money Mr. Tan had in two ways. First, since he had enough money to buy 80 pens, we have $T = 80C$. Second, since he bought 60 pens and had $51 left, we have $T = 60C + 51$.
3. Equating the Expressions
Now we can equate the two expressions for $T$: $$80C = 60C + 51$$
4. Solving for C
Next, we solve for $C$. Subtract $60C$ from both sides:$$80C - 60C = 51$$This simplifies to:$$20C = 51$$
5. Finding the Cost of Each Pen
Finally, divide both sides by 20 to find the cost of each pen:$$C = \frac{51}{20} = 2.55$$So, the cost of each pen is $2.55.
6. Final Answer
Therefore, the cost of each pen is $2.55.
### Examples
Imagine you are planning a school event and need to buy stationery. Knowing how to calculate the cost of individual items when given a total budget and leftover money helps you manage your expenses effectively. For example, if you know you have a budget for 100 pencils but only buy 75 and have $12.50 left, you can calculate the cost of each pencil to better plan your remaining purchases. This skill is useful in budgeting and making informed purchasing decisions.
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Rewritten by : Brahmana