Question

Ty has decided to go on a new cell phone plan. She makes $150 per month babysitting so she has to be careful of how much she spends on the plan. If the plan cost $55 per month plus $0.20 for each text, write an inequalilty to determine the maximum number of texts, t, she can make and still afford to pay the bill.Ty has decided to go on a new cell phone plan. She makes $150 per month babysitting so she has to be careful of how much she spends on the plan. If the plan cost $55 per month plus $0.20 for each text, write an inequalilty to determine the maximum number of texts, t, she can make and still afford to pay the bill.What is the inequality that determines the maximum number of texts, t, Ty can send while affording the cell phone plan, given that she makes $150 per month, the plan costs $55 per month, and each text costs $0.20?

Answer 1

The maximum number of texts Ty can send while affording the cell phone plan is 475.

Step-by-step explanation:

To determine the maximum number of texts, t, that Ty can send while affording the cell phone plan, we need to set up an inequality based on her income and the cost of the plan. The plan cost is $55 per month plus $0.20 for each text. Ty makes $150 per month babysitting. Let t represent the number of texts. The inequality we can write is: 55 + 0.20t ≤ 150.

To find the maximum number of texts, we can solve the inequality for t. First, subtract 55 from both sides of the inequality: 0.20t ≤ 95. Then, divide both sides of the inequality by 0.20: t ≤ 475.

Therefore, the maximum number of texts Ty can make and still afford to pay the bill is 475 texts.

Answer 2

Ty can send a maximum of 475 texts while affording the cell phone plan.

Let
`\( t \)` be the number of texts Ty can send. The total cost of the cell phone plan is the sum of the fixed monthly cost and the cost per text:

`\[ \text{Total cost} = \text{Fixed cost} + \text{Cost per text} * \text{Number of texts} \]`

Ty's monthly income is $150, and she wants to make sure she can afford the plan, so we set up the inequality:

`\[ 150 \geq 55 + 0.20t \]`

Step-by-step explanation:

- $150 is her monthly income.

- $55 is the fixed cost of the cell phone plan.

-
`\( 0.20t \)` is the cost of sending
`\( t \)` texts at $0.20 per text.

The inequality
`\( 150 \geq 55 + 0.20t \)` ensures that Ty's income is greater than or equal to the total cost of the cell phone plan, including the cost of texts. This way, she can afford the plan and have some money left from her babysitting income.

To find the maximum number of texts Ty can send while affording the cell phone plan, solve the inequality for
`\( t \)`:

`\[ 150 \geq 55 + 0.20t \]`

Subtract 55 from both sides:

`\[ 95 \geq 0.20t \]`

Divide by 0.20:

`\[ t \leq (95)/(0.20) \]`

Simplify:

`\[ t \leq 475 \]`