A bouquet of flowers costs $17.95. If a customer has a coupon that allows him to save $3.75 on the price of the flowers, how much will he pay for the flowers?
Of the 600 people at a music festival, 420 had attended the previous year. How many people out of 100 had attended the previous year?
The Correct Answer and Explanation is :
Answers & Explanation:
1. Discounted Price of Flowers
The original price of the bouquet is $17.95. The customer has a coupon that provides a discount of $3.75. To determine the final cost, we subtract the discount from the original price:
[
17.95 – 3.75 = 14.20
]
So, after using the coupon, the customer will pay $14.20 for the flowers.
2. Proportion of Returning Attendees
We are given that out of 600 people at a music festival, 420 had attended the previous year. To find how many people out of 100 had attended before, we set up a proportion:
[
\frac{420}{600} = \frac{x}{100}
]
Solving for ( x ), we multiply:
[
x = \left(\frac{420}{600}\right) \times 100
]
[
x = 70
]
So, 70 out of every 100 people at the festival had attended the previous year.
Explanation (300 words)
Discounted Price of Flowers
When calculating the final price after applying a discount, we use simple subtraction. The original bouquet cost is $17.95, and the discount is $3.75. By subtracting the discount, we get $14.20. This concept is widely used in shopping, where discounts and coupons reduce the amount a customer pays.
Music Festival Attendance
In problems involving proportions, we use the concept of ratios. Here, 420 out of 600 people had attended before. To determine the number per 100, we convert this ratio into a fraction:
[
\frac{420}{600}
]
By multiplying by 100, we adjust the ratio to a scale of 100. The result, 70 out of 100, shows that 70% of the attendees were returning visitors. This percentage helps understand attendance trends and predict future participation.
These concepts—percentage calculations and price reductions—are essential in real-world applications like budgeting, marketing, and event planning.
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