Proportional and Nonproportional Relationships

A teacher is planning a year-end pizza party for her students. Ace Pizza offers free delivery and charges $8 for each medium pizza. Warm-Up Pizzas Ordered 1234 Cost ($) Copy and complete the table to determine the cost for different numbers of pizza ordered For each number of pizzas, write the relationship of the cost and number of pizzas as a ratio in simplest form. What do you notice?

Proportional and Nonproportional Relationships In the warm-up, notice that while the number of pizzas ordered and the cost both change or vary, the ratio of these quantities remains the same, a constant $8 per pizza. cost of order pizzas ordered or $8 per pizza This relationship is expressed by saying that the cost of an order is proportional to the number of pizzas ordered. = = = =

Proportional and Nonproportional Relationships If two quantities are proportional, then they have a constant ratio. For relationships in which the ratio is not constant, the two quantities are said to be nonproportional. Si dos magnitudes son proporcionales, a continuación, que tienen una relación constante. Para las relaciones en las que la relación no es constante, las dos cantidades se dice que son no proporcional. Record the definitions in your math journal on page P.

Identify Proportional Relationships Uptown Pizza sells medium pizzas for $7 each but charges $3 delivery fee per order. Is the cost of an order proportional to the number of pizzas ordered? Find the cost for 1, 2, 3, and 4 pizzas and make a table to display numbers and cost. Pizzas Ordered1234 Cost ($)

For each number of pizzas, write the relationship of the cost and number of pizzas as a ratio in simplest form. cost of order pizzas ordered Since the ratios of the two quantities are not the same, the cost of an order is not proportional to the number of pizzas ordered. The relationship is nonproportional. or 10 or 8 or 8.5 or 7.75

Example Problem At the beginning of the school year, Isabel had $120 in the bank. Each week, she deposits another $20. Is her account balance proportional to the number of weeks since she started school? Balance$120$140 Week12

Example Problem An adult elephant drinks about 225 liters of water each day. Is the number of days that an elephant’s water supply lasts proportional to the number of liters of water the elephant drinks?

Example Problem The Vista Marina rents boats for $25 per hour. In addition to the rental fee, there is a $12 charge for fuel. Is the number of hours you can rent the boat proportional to the total cost?

Example Problem This year Christine celebrated her 10 th birthday, and her brother Jared celebrated his 5 th birthday. Christine notes that she was twice as old as her brother was. Is the relationship between their ages proportional? Explain your reasoning using a table of values.

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