When Margo makes cheese ravioli, she uses both ricotta and mozzarella cheeses to make the filling. She often varies the proportions of the cheeses that she uses, but the number of ounces of ricotta cheese, r, is always more than 3 times the number of ounces of mozzarella cheese, m. For one batch of ravioli that Margo makes, she spends less than $8 on the cheeses. The ricotta cheese costs $0.24 per ounce, and the mozzarella cheese costs $0.15 per ounce. For which of the following systems of inequalities do the positive solutions represent all possible combinations of numbers of ounces of ricotta and mozzarella cheeses that Margo could have used for this batch?

When Margo makes cheese ravioli, she uses both ricotta and mozzarella cheeses to make the filling. She often varies the proportions of the cheeses that she uses, but the number of ounces of ricotta cheese, r, is always more than 3 times the number of ounces of mozzarella cheese, m. For one batch of ravioli that Margo makes, she spends less than $8 on the cheeses. The ricotta cheese costs $0.24 per ounce, and the mozzarella cheese costs $0.15 per ounce. For which of the following systems of inequalities do the positive solutions represent all possible combinations of numbers of ounces of ricotta and mozzarella cheeses that Margo could have used for this batch?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

When Margo makes cheese ravioli, she uses both ricotta and mozzarella cheeses to make the filling. She often varies the proportions of the cheeses that she uses, but the number of
ounces of ricotta cheese, r, is always more than 3 times the number of ounces of mozzarella cheese, m. For one batch of ravioli that Margo makes, she spends less than $8 on the
cheeses. The ricotta cheese costs $0.24 per ounce, and the mozzarella cheese costs $0.15 per ounce. For which of the following systems of inequalities do the positive solutions
represent all possible combinations of numbers of ounces of ricotta and mozzarella cheeses that Margo could have used for this batch?
m> 3r
A
0.15r + 0.24m < 8
Sr> 3m
0.15r + 0.24m < 8
m> 3r
C
10.24r + 0.15m < 8
Sr> 3m
D
0.24r + 0.15m < 8
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