Select The Equation That Matches The Following Story:A Family Of 3 Goes To A Fair. Tickets Cost $\$5$ Each, But Each Person Has A Coupon. They Pay $\$7$ Altogether.How Much Money Does Each Person Save On Buying Their Ticket?Options:A.

Feb 26, 2025 by ADMIN 235 views

Introduction

Mathematics is a subject that is often associated with numbers, equations, and formulas. However, it is also a subject that is deeply connected to real-life scenarios and everyday situations. In this article, we will explore a story about a family of three who go to a fair and use coupons to buy tickets. We will then use mathematical equations to determine how much money each person saves on buying their ticket.

The Story

A family of three goes to a fair. Tickets cost $\$5$ each, but each person has a coupon. They pay $\$7$ altogether. The question is, how much money does each person save on buying their ticket?

Understanding the Problem

To solve this problem, we need to understand the concept of coupons and how they affect the cost of buying tickets. A coupon is a discount that is applied to the original price of an item. In this case, the coupon is worth $\$2$ off the original price of $\$5$ per ticket.

Setting Up the Equation

Let's denote the original price of a ticket as $P$ , the discount offered by the coupon as $D$ , and the number of people in the family as $N$ . We are given that $P = \$5$ and $D = \$2$ . We are also given that the family pays $\$7$ altogether.

Writing the Equation

We can write an equation to represent the situation:

NP - ND = 7

This equation states that the total cost of buying $N$ tickets at the original price $P$ minus the total discount offered by the coupon $D$ is equal to the amount the family pays.

Solving the Equation

We can simplify the equation by substituting the values of $P$ and $D$ :

5N - 2N = 7

This simplifies to:

3N = 7

Finding the Value of N

To find the value of $N$ , we can divide both sides of the equation by 3:

N = \frac{7}{3}

However, this is not possible since the number of people in the family must be a whole number. Therefore, we need to re-examine our equation.

Re-examining the Equation

Let's go back to the original equation:

NP - ND = 7

We can rewrite this equation as:

(P - D)N = 7

Substituting the values of $P$ and $D$ , we get:

(5 - 2)N = 7

This simplifies to:

3N = 7

However, this is still not possible since the number of people in the family must be a whole number. Therefore, we need to re-examine our assumptions.

Re-examining the Assumptions

Let's re-examine our assumptions about the problem. We assumed that the family pays $\$7$ altogether, but we also assumed that each person has a coupon. However, we did not assume that the coupons are used to buy tickets. Therefore, we need to re-examine our equation.

Re-writing the Equation

Let's re-write the equation to reflect the fact that the coupons are not used to buy tickets:

NP = 7

This equation states that the total cost of buying $N$ tickets at the original price $P$ is equal to the amount the family pays.

Solving the Equation

We can substitute the value of $P$ into the equation:

5N = 7

This simplifies to:

N = \frac{7}{5}

However, this is not possible since the number of people in the family must be a whole number. Therefore, we need to re-examine our equation.

Re-examining the Equation

Let's re-examine our equation:

NP = 7

We can rewrite this equation as:

In our previous article, we explored a story about a family of three who go to a fair and use coupons to buy tickets. We used mathematical equations to determine how much money each person saves on buying their ticket. However, we encountered some difficulties in solving the equation. In this article, we will provide a Q&A section to help clarify any confusion and provide additional insights.

Q: What is the original price of a ticket?

A: The original price of a ticket is $\$5$ .

Q: What is the discount offered by the coupon?

A: The discount offered by the coupon is $\$2$ .

Q: How much money does each person save on buying their ticket?

A: To determine how much money each person saves on buying their ticket, we need to use the equation:

NP - ND = 7

However, we need to re-examine our assumptions about the problem.

Q: What are the assumptions about the problem?

A: We assumed that the family pays $\$7$ altogether, but we also assumed that each person has a coupon. However, we did not assume that the coupons are used to buy tickets.

Q: How can we re-write the equation to reflect the fact that the coupons are used to buy tickets?

A: We can re-write the equation as:

NP - ND = 7

However, this equation is still not correct. We need to re-examine our assumptions.