Complete the following two problems.
Problem 1
The table shows the number of greeting cards that Americans buy for various occasions.
Holiday/Event Cards Sold
Valentine’s Day 900 million
Mother’s Day 150 million
Father’s Day 95 million
Graduation 60 million
Thanksgiving 30 million
Halloween 25 million
Source: Hallmark Cards
Use the information to answer the following: Explain how you might use the information in the table if you owned a shop selling gifts and greeting cards.
Problem 2
Solve each proportion to find the unknown number. Round your answers to hundredths when necessary:
a. 8/x = 24/30
b. 0.7/9.8 = 3.6/x
c. 250/24.8 = x/1.75
d. x/3.6 = 4.5/6
Problem 1: If you owned a shop selling gifts and greeting cards, you can use the information in the table to make informed decisions about your inventory management and marketing strategies. Here's how you can utilize the information:
1. Stocking up: By knowing the number of greeting cards sold for various occasions, you can estimate the demand during specific times of the year. For example, since Valentine's Day is a popular event with 900 million cards sold, you would want to make sure you have an adequate supply of Valentine's Day cards in stock to meet the demand.
2. Marketing campaigns: You can align your marketing efforts with the occasions that have a high demand for greeting cards. For instance, you can create special promotions or discounts for Mother's Day, as it has a demand for 150 million cards. This can help attract customers to your shop and increase sales.
3. Assortment planning: The data can guide you in determining the assortment of cards you should offer in your shop. You can analyze the table to identify which occasions have the highest card sales and prioritize stocking a wider variety of cards for those events.
4. Insights for expansion: The information in the table can also help you make decisions about expanding your business. For example, if you notice a significant increase in the number of cards sold for Graduation, you might consider adding graduation-themed gifts and cards to your inventory to cater to this growing market.
By using the provided data, you can strategically plan your inventory, target your marketing efforts, and optimize your business operations to increase your shop's profitability.
Problem 2: Let's solve each proportion to find the unknown numbers:
a. 8/x = 24/30
To solve this proportion, we can use cross multiplication.
8 * 30 = 24 * x
240 = 24x
To isolate x, divide both sides of the equation by 24.
x = 240/24 = 10
b. 0.7/9.8 = 3.6/x
Similarly, we use cross multiplication to solve for x.
0.7 * x = 3.6 * 9.8
0.7x = 35.28
Divide both sides by 0.7 to isolate x.
x = 35.28/0.7 = 50.4
c. 250/24.8 = x/1.75
Cross multiplying gives us:
250 * 1.75 = 24.8 * x
437.5 = 24.8x
Divide both sides by 24.8 to solve for x.
x = 437.5/24.8 = 17.62
d. x/3.6 = 4.5/6
Cross multiplying gives:
x * 6 = 4.5 * 3.6
6x = 16.2
Divide both sides by 6 to solve for x.
x = 16.2/6 = 2.7
The unknown numbers are:
a. x = 10
b. x ≈ 50.4 (rounded to hundredths)
c. x ≈ 17.62 (rounded to hundredths)
d. x = 2.7