Riley is solving a problem to find the number of tents comma sleeping bags comma and backpacks that she should order. She wrote a system of equations and solved the system. She found that her general solution was (x comma y comma z) equals (15 minus 3 z comma 20 plus 2 z comma z) How many solutions are there to her problem?

Question

Hugh Lucero

Mathematics

6 May, 13:26

Riley is solving a problem to find the number of tents comma sleeping bags comma and backpacks that she should order. She wrote a system of equations and solved the system. She found that her general solution was (x comma y comma z) equals (15 minus 3 z comma 20 plus 2 z comma z) How many solutions are there to her problem?

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Answers (1)

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Moriah Larsen · Answer 1

6

Step-by-step explanation:

If we place no restrictions on the values of the variables, there are an infinite number of possible solutions.

In this scenario, it is reasonable to require all variables have non-negative integer values. That restricts the solutions to ...

(x, y, z) ∈ { (15, 20, 0), (12, 22, 1), (9, 24, 2), (6, 26, 3), (3, 28, 4), (0, 30, 5) }

There are 6 solutions to her problem.