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A phone company offers two monthly charge plans. In plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In plan B, the customer pays a monthly fee of $11.40 and then an additional 6 cents per minute of use. For what amounts of monthly phone use will plan A cost at least as much as plan B? Use m for the number of minutes of phone use in a month, and solve your inequality for m.

Respuesta :

SOLUTION

In plan A, the charge is

[tex]8\text{cent per minutes with no monthly fe}e[/tex]

For Plan B, the company charge

[tex]\text{ \$11.40 per month +6 cent per minutes }[/tex]

Since the Number of minutes is m

The amount of monthly phone use in plan A is

[tex]\begin{gathered} \text{ 8m cent } \\ 0.08m\text{ dollar} \end{gathered}[/tex]

The amount of monthly phone use in plan B is

[tex]\begin{gathered} \text{ \$11.40+0.06m} \\ \sin ce\text{ 100 cent=\$1} \\ 6\text{cent}=\text{ \$0.06} \end{gathered}[/tex]

The amounts of monthly phone use of plan A cost at least as much as plan B

will be

[tex]\begin{gathered} \text{The amount of Plan A }\ge\text{ The amount of plan B} \\ 0.08m\ge11.40+0.06m \end{gathered}[/tex]

Then, by collecting like terms, we have

[tex]\begin{gathered} 0.08m-0.06m\ge11.40 \\ 0.02m\ge11.40 \\ m\ge\frac{11.40}{0.02} \\ m\ge570 \end{gathered}[/tex]