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# How a Clothing Business Finds a Linear Relationship Between Price and Number of Shirts Solved

A clothing business finds a linear relationship between the number of shirts sold and the price per shirt. They can sell 5000 shirts for \$30 and sell 3,000 shirts for \$20. However, they must also find the equation for nn shirts. To do this, they use historical data. For example, if a company sells 5,000 t-shirts at \$10 each, it can sell those same t-shirts for \$66 each. To solve this problem, they need to calculate a linear equation with these variables.

A farmer finds a linear relationship between the number of bean stalks he plants and the yield. He plants thirty, 34, and 28 stalks, and finds that the yield is equal to y=mn+b. However, if the farmer grows more than n stalks, he can find that the yield is higher. The linear relationship between price and yield is interpreted as y=mn+b.

If a farmer plants thirty, 34, and 28 stalks, he finds a linear relationship between the yield and n. Then, if the farmer plants 30 stalks, he will receive the same yield as if he planted thirty, 34, and 28 stalks. In other words, the slope reflects a 10% increase over the next decade. Similarly, a clothing business finds there is a high correlation between prices and number of sales.

The population of a town has been increasing linearly since 1960. The town population in 1990 was 287,900, but it increased by 1,700 each year. In t years, the population will be 497,000. Therefore, the slope of the linear function is I(x)=1054n+23,286. Then, a person should interpret the slope as a \$1054 increase over ten years.

A clothing business is a good example of a linear relationship. A farmer’s income is related to the number of stalks he plants. He should plant thirty stalks if he wants a large crop. It will be worth planting more if he can increase his yield. For the city of Seattle, the population increased from two87,500 in 1960 to 275,900 in 1989.

A farmer finds a linear relationship between the number of bean stalks planted and the yield. He plants thirty stalks and twenty stalks, but he finds a relationship between n and the number of stalks. The slope is -0.007. The average annual income of a town was \$1054 in 1990. Today, it has grown by a similar rate. If n is equal to 83, the average income will increase by \$23,280 over the same period of time.

The number of stalks planted determines the yield. If a farmer plants thirty stalks, he will reap 30 stalks. If he plants thirty stalks, he will produce twenty-eight stalks. So, a farmer’s income is a function of n. The slope coefficient is -0.007. If n is equal to ten years, he has the same average income as a farmer in another town.

The population of a town has been growing linearly. It was 45,000 people in 1990, and will continue to grow by a thousand people per year for t years. A clothing business is also given a linear relationship between the price and the number of employees. For example, if a person has two employees, she is more likely to earn \$100 than one employee. In contrast, if a woman wears a dress with her pants, she will make a larger profit in a smaller town.

A clothing business finds that the price of a product is a linear function of the number of items sold. The cost per unit of a dress will be influenced by the number of people wearing the same type of blouse. It will also be affected by the color of the dress. For example, a shirt sold for \$10 in 1990 will sell for more than double its value in five years. And vice versa.

How a Clothing Business Finds a Linear Relationship Between Price and Number of Shirts Solved
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