Ratios and Proportional Relationships Flashcards

A grocery store sells two different sizes of orange juice. A 64-ounce carton costs $3.84, and a 96-ounce carton costs $5.28. Which of the following statements is true about the price of the orange juice?

Answer: The 96-ounce carton costs $0.055 per ounce.

To determine the best value, calculate the unit price (cost per ounce) for each carton. For the 64-oz carton: $3.84 / 64 oz = $0.06 per ounce. For the 96-oz carton: $5.28 / 96 oz = $0.055 per ounce. Comparing the unit prices, the 96-ounce carton costs less per ounce ($0.055) than the 64-ounce carton ($0.06), making it the better value.

A car travels at a constant speed. The relationship between the distance traveled (d) in miles and the time (t) in hours is represented by the equation d = 55t. What is the constant of proportionality in this relationship?

Answer: 55

A proportional relationship can be represented by the equation y = kx, where 'k' is the constant of proportionality. In the given equation, d = 55t, 'd' is equivalent to 'y', 't' is equivalent to 'x', and 55 is the constant value 'k' that relates the two variables. It represents the unit rate, which is 55 miles per hour.

A recipe for a batch of 12 cookies requires 1 1/2 cups of flour. A baker wants to make 30 cookies. How many cups of flour will the baker need?

Answer: 3 3/4 cups

First, find the amount of flour per cookie (the unit rate). Divide the total flour by the number of cookies: (1 1/2) / 12 = (3/2) / 12 = 3/2 * 1/12 = 3/24 = 1/8 cup of flour per cookie. Then, multiply the unit rate by the desired number of cookies: 1/8 * 30 = 30/8 = 15/4 = 3 3/4 cups.

The graph below shows the relationship between the number of hours a plumber works and the total amount they charge. Which statement correctly interprets the point (2, 150) on the graph?

Answer: The plumber works for 2 hours and charges $150.

On a graph of a proportional relationship, a point (x, y) represents the relationship between the two quantities. The x-axis typically represents the independent variable (hours worked) and the y-axis represents the dependent variable (total charge). Therefore, the point (2, 150) means that for 2 hours of work (x-value), the total charge is $150 (y-value).

Last year, a local library had 8,000 books. This year, the number of books increased by 5%. How many books does the library have now?

Answer: 8,400 books

To find the number of new books, calculate 5% of 8,000: 0.05 * 8,000 = 400 books. This is the amount of the increase. Add this increase to the original number of books to find the new total: 8,000 + 400 = 8,400 books. Alternatively, you can multiply the original amount by 105% (100% + 5%): 8,000 * 1.05 = 8,400 books.

Which of the following tables represents a proportional relationship between x and y?

Answer: x: 3, 6, 9, 12; y: 1, 2, 3, 4

A relationship is proportional if the ratio of y to x (y/x) is constant for all pairs of values. Let's check the ratios for the correct table: 1/3, 2/6 = 1/3, 3/9 = 1/3, 4/12 = 1/3. Since the ratio y/x is consistently 1/3, this table shows a proportional relationship with a constant of proportionality of 1/3.