A restaurant needs to plan seating for a party of 150 people. Large tables seat 10 people and small tables seat 6. Let x represent the number of large tables and y represent the number of small tables. The expression 10A + 6B, which represents the total number of people you can seat using A large tables and B small tables, is called a linear combination. For instance, 150 people could be seated using 12 large tables and 5 small tables. Use that expression to enter an equation in standard form that models all the different combinations of tables the restaurant could use. Then identify at least one possible combination of tables other than (12, 5).

Question

Mathematics

Ronan Roth

11 June, 02:35

A restaurant needs to plan seating for a party of 150 people. Large tables seat 10 people and small tables seat 6. Let x represent the number of large tables and y represent the number of small tables. The expression 10A + 6B, which represents the total number of people you can seat using A large tables and B small tables, is called a linear combination. For instance, 150 people could be seated using 12 large tables and 5 small tables. Use that expression to enter an equation in standard form that models all the different combinations of tables the restaurant could use. Then identify at least one possible combination of tables other than (12, 5).

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Answers (1)

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Butterball · Answer 1

A=0, 3, 6, 9, 12, 15

B=25, 20, 15, 10, 5, 0

Step-by-step explanation:

10*A + 6*B = 150

B=150/6 - (10 * A / 6) = 25 - (5 * A / 3)

A should be one of the multiple of 3

A=0, 3, 6, 9, 12, 15

B=25, 20, 15, 10, 5, 0

Ans: (0, 25) or (3, 20) or (6, 15) or (9, 10) or (15, 0)