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Question Arianna's cell plan has a flat cost of $54.50\$54.50 per month and $5\$5 per gigabyte. She wants to keep her bill under $75\$75 per month. Find the maximum number of gigabytes gg she can use.

Studdy Solution

STEP 1

Assumptions1. Arianna pays a flat cost of 54.50permonth..Shepaysanadditional54.50 per month. . She pays an additional 5 per gigabyte of data used.
3. She wants to keep her total bill under 75permonth.<br/>4.Weneedtofindthemaximumnumberofgigabytes,75 per month.<br />4. We need to find the maximum number of gigabytes, g$, she can use while staying within her budget.

STEP 2

First, we need to write an inequality that represents the situation. The total cost is the sum of the flat cost and the cost per gigabyte, which must be less than or equal to $75.
Flat cost+Cost per gigabyte×g≤Total budgetFlat\, cost + Cost\, per\, gigabyte \times g \leq Total\, budget

STEP 3

Now, plug in the given values for the flat cost, cost per gigabyte, and total budget to form the inequality.
$54.50+$5g≤$75\$54.50 + \$5g \leq \$75

STEP 4

Next, we need to isolate gg in the inequality to find the maximum number of gigabytes Arianna can use. Start by subtracting the flat cost from both sides of the inequality.
$g≤$75−$54.50\$g \leq \$75 - \$54.50

STEP 5

Calculate the right side of the inequality.
$5g≤$20.50\$5g \leq \$20.50

STEP 6

Finally, divide both sides of the inequality by the cost per gigabyte to solve for gg.
g≤$20.50/$5g \leq \$20.50 / \$5

STEP 7

Calculate the right side of the inequality to find the value of gg.
g≤4.1g \leq4.1Arianna can use up to4.1 gigabytes of data to keep her bill under $75 per month.

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