Question
Under his cell phone plan, Ian pays a flat cost of $44.50 per month and $5 per gigabyte. He wants to keep his bill at $61 per month. Which equation could be used to determine xx, the number of gigabytes of data Ian can use while staying within his budget?
Answer
Multiple Choice Answers
x, equals, start fraction, 6, 1, minus, 44, point, 5, divided by, 5, end fractionx=
5
2
1
2
1
61−44.5
5, x, equals, 44, point, 5, minus, 615x=44.5−61
61, equals, 5, plus, 44, point, 5, x61=5+44.5x
x, equals, start fraction, 6, 1, minus, 5, divided by, 44, point, 5, end fractionx=
44.5
2
1
2
1
61−5
Answer
Multiple Choice Answers
x, equals, start fraction, 6, 1, minus, 44, point, 5, divided by, 5, end fractionx=
5
2
1
2
1
61−44.5
5, x, equals, 44, point, 5, minus, 615x=44.5−61
61, equals, 5, plus, 44, point, 5, x61=5+44.5x
x, equals, start fraction, 6, 1, minus, 5, divided by, 44, point, 5, end fractionx=
44.5
2
1
2
1
61−5
Answers
GPT-4o mini
To determine the number of gigabytes of data (x) Ian can use while keeping his bill at or below $61 per month, we can set up the following equation based on his plan:
1. He has a flat cost of $44.50.
2. He pays an additional $5 per gigabyte of data.
The total cost (C) can be expressed as:
\[ C = 44.50 + 5x \]
We want to find the maximum number of gigabytes \( x \) such that the total cost does not exceed $61. Thus, we set up the inequality:
\[ 44.50 + 5x \leq 61 \]
To find the equation, we can convert the inequality into an equation by setting it equal to 61, which gives us:
\[ 44.50 + 5x = 61 \]
Now, to isolate \( x \), we can rearrange this equation:
1. Subtract 44.50 from both sides:
\[ 5x = 61 - 44.50 \]
\[ 5x = 16.50 \]
2. Now, divide by 5:
\[ x = \frac{16.50}{5} \]
So the equation we derived above can be expressed as:
\[ x = \frac{61 - 44.50}{5} \]
Looking at the multiple choice answers you provided, the correct answer is:
\[ x = \frac{61 - 44.5}{5} \]
This option is the correct representation of the relationship between the flat cost, the cost per gigabyte, and the total cost limit.
1. He has a flat cost of $44.50.
2. He pays an additional $5 per gigabyte of data.
The total cost (C) can be expressed as:
\[ C = 44.50 + 5x \]
We want to find the maximum number of gigabytes \( x \) such that the total cost does not exceed $61. Thus, we set up the inequality:
\[ 44.50 + 5x \leq 61 \]
To find the equation, we can convert the inequality into an equation by setting it equal to 61, which gives us:
\[ 44.50 + 5x = 61 \]
Now, to isolate \( x \), we can rearrange this equation:
1. Subtract 44.50 from both sides:
\[ 5x = 61 - 44.50 \]
\[ 5x = 16.50 \]
2. Now, divide by 5:
\[ x = \frac{16.50}{5} \]
So the equation we derived above can be expressed as:
\[ x = \frac{61 - 44.50}{5} \]
Looking at the multiple choice answers you provided, the correct answer is:
\[ x = \frac{61 - 44.5}{5} \]
This option is the correct representation of the relationship between the flat cost, the cost per gigabyte, and the total cost limit.