QuestionYou have a 60-minute trial. Setup takes $5 \frac{1}{6}$ mins, each level $7 \frac{1}{3}$ mins. Which inequality for levels $\ell$ ?
A $5 \frac{1}{6}+\left(7 \frac{1}{3}\right) \ell \geq 60$ B $5 \frac{1}{6}+\left(7 \frac{1}{3}\right) \ell \leq 60$ C $\left(7 \frac{1}{3}\right) \ell-5 \frac{1}{6} \geq 60$ D $\left(7 \frac{1}{3}\right) \ell-5 \frac{1}{6} \leq 60$
Can you play 6 levels for free?

Studdy Solution

STEP 1

Assumptions1. The total free trial time is60 minutes. . The time to set up the game is $5 \frac{1}{6}$ minutes.
3. The time to play each level is $7 \frac{1}{3}$ minutes.
4. The setup time is a one-time cost, not recurring for each level.
5. The number of levels, $\ell$ , is what we want to find.

STEP 2

We need to create an inequality that represents the total time spent on the game. This includes the setup time and the time spent playing each level. The total time should not exceed the free trial time of60 minutes.
$Setup\, time + (Time\, per\, level \\times Levels) \leq Total\, trial\, time$

STEP 3

Now, plug in the given values for the setup time, time per level, and total trial time to form the inequality.
$5 \frac{1}{6} + \left(7 \frac{1}{3}\right) \ell \leq60$ So, the correct inequality is (B) $5 \frac{1}{6}+\left(7 \frac{1}{3}\right) \ell \leq60$ .

STEP 4

To find out if you can play6 levels during your free trial, plug $\ell =6$ into the inequality.
$\frac{1}{6} + \left(7 \frac{1}{3}\right) \times6 \leq60$

STEP 5

First, calculate the time spent playing levels.
$\left(7 \frac{1}{3}\right) \times =44$

STEP 6

Then, add the setup time to the time spent playing6 levels.
$5 \frac{1}{6} +44 =49 \frac{1}{6}$

STEP 7

Check if the total time spent is less than or equal to the total trial time.
$49 \frac{1}{6} \leq60$ Since $49 \frac{1}{6}$ is less than60, you can play6 levels during your free trial.

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Studdy Solution

STEP 1

Assumptions1. The total free trial time is60 minutes. . The time to set up the game is $5 \frac{1}{6}$ minutes.
3. The time to play each level is $7 \frac{1}{3}$ minutes.
4. The setup time is a one-time cost, not recurring for each level.
5. The number of levels, $\ell$ , is what we want to find.

STEP 2

We need to create an inequality that represents the total time spent on the game. This includes the setup time and the time spent playing each level. The total time should not exceed the free trial time of60 minutes.
$Setup\, time + (Time\, per\, level \\times Levels) \leq Total\, trial\, time$

STEP 3

Now, plug in the given values for the setup time, time per level, and total trial time to form the inequality.
$5 \frac{1}{6} + \left(7 \frac{1}{3}\right) \ell \leq60$ So, the correct inequality is (B) $5 \frac{1}{6}+\left(7 \frac{1}{3}\right) \ell \leq60$ .

STEP 4

To find out if you can play6 levels during your free trial, plug $\ell =6$ into the inequality.
$\frac{1}{6} + \left(7 \frac{1}{3}\right) \times6 \leq60$

STEP 5

First, calculate the time spent playing levels.
$\left(7 \frac{1}{3}\right) \times =44$

STEP 6

Then, add the setup time to the time spent playing6 levels.
$5 \frac{1}{6} +44 =49 \frac{1}{6}$

STEP 7

Check if the total time spent is less than or equal to the total trial time.
$49 \frac{1}{6} \leq60$ Since $49 \frac{1}{6}$ is less than60, you can play6 levels during your free trial.

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Studdy Solution

STEP 1

STEP 2

STEP 3

STEP 4

To find out if you can play6 levels during your free trial, plug ℓ=6\ell =6ℓ=6 into the inequality.16+(713)×6≤60 \frac{1}{6} + \left(7 \frac{1}{3}\right) \times6 \leq6061​+(731​)×6≤60

STEP 5

First, calculate the time spent playing levels.(713)×=44\left(7 \frac{1}{3}\right) \times =44(731​)×=44

STEP 6

Then, add the setup time to the time spent playing6 levels.516+44=49165 \frac{1}{6} +44 =49 \frac{1}{6}561​+44=4961​

STEP 7

Check if the total time spent is less than or equal to the total trial time.4916≤6049 \frac{1}{6} \leq604961​≤60Since 491649 \frac{1}{6}4961​ is less than60, you can play6 levels during your free trial.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

To find out if you can play6 levels during your free trial, plug $\ell =6$ into the inequality.
$\frac{1}{6} + \left(7 \frac{1}{3}\right) \times6 \leq60$

First, calculate the time spent playing levels.
$\left(7 \frac{1}{3}\right) \times =44$

Then, add the setup time to the time spent playing6 levels.
$5 \frac{1}{6} +44 =49 \frac{1}{6}$

Check if the total time spent is less than or equal to the total trial time.
$49 \frac{1}{6} \leq60$ Since $49 \frac{1}{6}$ is less than60, you can play6 levels during your free trial.