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Janae has a soap bottle that has 474 ml of liquid soap. Each push of the pump uses 8 ml. of soap. There needs to be at least 50 ml. of soap in the bottle for the pump to work• Write and solve an inequality that represents the number of pushes of the pump possible before the pump stops working.Write a sentence to represent the solution set in the context of the problem.Show your workRespond in the space provided.

Respuesta :

Let's use the variable x to represent the number of pushes in the pump.

The initial amount is 474 ml, each push decreases this amount in 8 ml, and the minimum amount is 50 ml, so we can write the following inequality:

[tex]474-8x\ge50[/tex]

Solving this inequality for x, we have:

[tex]\begin{gathered} -8x\ge50-474 \\ -8x\ge-424 \\ 8x\le424 \\ x\le\frac{424}{8} \\ x\le53 \end{gathered}[/tex]

So the maximum number of pushes is 53. The solution set is x <= 53.

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