Carol Sells Handmade Greeting Cards For $\$15$ Each. She Sold $x$ Cards On Monday. On Tuesday, She Sold 4 Fewer Cards Than On Monday. On Wednesday, She Sold 6 More Cards Than On Monday. Over These Three Days, She Earned A Total Of

Introduction

In this article, we will explore the sales of handmade greeting cards by Carol over a period of three days. We will use mathematical expressions to represent the number of cards sold and the total earnings. Our goal is to understand how Carol's sales varied over these three days and what factors contributed to her total earnings.

Monday's Sales

On Monday, Carol sold $x$ cards. Each card was sold for $\$15$. Therefore, the total earnings from Monday's sales can be represented as:

$$\text{Monday's earnings} = 15x$$

Tuesday's Sales

On Tuesday, Carol sold 4 fewer cards than on Monday. This means she sold $x - 4$ cards. The total earnings from Tuesday's sales can be represented as:

$$\text{Tuesday's earnings} = 15(x - 4)$$

Wednesday's Sales

On Wednesday, Carol sold 6 more cards than on Monday. This means she sold $x + 6$ cards. The total earnings from Wednesday's sales can be represented as:

$$\text{Wednesday's earnings} = 15(x + 6)$$

Total Earnings

The total earnings over these three days can be found by adding the earnings from each day:

$$\text{Total earnings} = 15x + 15(x - 4) + 15(x + 6)$$

Simplifying the expression, we get:

$$\text{Total earnings} = 15x + 15x - 60 + 15x + 90$$

Combine like terms:

$$\text{Total earnings} = 45x + 30$$

Understanding the Total Earnings

The total earnings expression can be broken down into two parts: $45x$ and $30$. The $45x$ term represents the total earnings if Carol sold $x$ cards on each day. The $30$ term represents the fixed earnings that Carol received from selling cards on Tuesday and Wednesday.

Graphical Representation

To visualize the total earnings, we can create a graph. Let's assume that Carol sold $x = 0$ cards on Monday. The graph will show the total earnings for different values of $x$.

$x$	Monday's earnings	Tuesday's earnings	Wednesday's earnings	Total earnings
0	0	0	0	30
1	15	11	21	47
2	30	22	42	94
3	45	33	63	141
4	60	44	84	188
5	75	55	105	235

Conclusion

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Introduction

In our previous article, we explored the sales of handmade greeting cards by Carol over a period of three days. We used mathematical expressions to represent the number of cards sold and the total earnings. In this article, we will answer some frequently asked questions related to Carol's sales.

Q: What is the total earnings expression?

A: The total earnings expression is $45x + 30$, where $x$ represents the number of cards sold on Monday.

Q: What does the $45x$ term represent?

A: The $45x$ term represents the total earnings if Carol sold $x$ cards on each day.

Q: What does the $30$ term represent?

A: The $30$ term represents the fixed earnings that Carol received from selling cards on Tuesday and Wednesday.

Q: How can I calculate the total earnings for a given value of $x$?

A: To calculate the total earnings for a given value of $x$, simply substitute the value of $x$ into the total earnings expression: $45x + 30$.

Q: What is the minimum number of cards that Carol needs to sell to earn a total of $\$30$?

A: To find the minimum number of cards that Carol needs to sell to earn a total of $\$30$, set the total earnings expression equal to $30$ and solve for $x$:

$$45x + 30 = 30$$

Subtract 30 from both sides:

$$45x = 0$$

Divide both sides by 45:

$$x = 0$$

Therefore, Carol needs to sell at least 0 cards on Monday to earn a total of $\$30$.

Q: What is the maximum number of cards that Carol can sell to earn a total of $\$300$?

A: To find the maximum number of cards that Carol can sell to earn a total of $\$300$, set the total earnings expression equal to 300 and solve for $x$:

$$45x + 30 = 300$$

Subtract 30 from both sides:

$$45x = 270$$

Divide both sides by 45:

$$x = 6$$

Therefore, Carol can sell at most 6 cards on Monday to earn a total of $\$300$.

Q: How can I graph the total earnings expression?

A: To graph the total earnings expression, use a graphing calculator or software to plot the function $y = 45x + 30$. The graph will show the total earnings for different values of $x$.

Conclusion

In this article, we answered some frequently asked questions related to Carol's sales. We hope that this Q&A article has provided you with a better understanding of the total earnings expression and how to calculate the total earnings for a given value of $x$.