Question

Stefan spends $6.50 on supplies for a lemonade stand and sells each cup of lemonade for $1.25. What is x, the number of cups of lemonade Stefan must sell to earn a profit of more than $50?

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Stefan has a balance of $6.50 in his savings account and deposits $1.25 each week. What is x, the number of weeks Stefan must deposit $1.25 in order to have a balance of more than $50 in his savings account?
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Stefan earns 1.25% interest on the balance in his checking account and has to pay a monthly charge of $6.50. What is x, the balance that Stefan must have in his checking account in order to have an ending balance greater than $50 after interest and fees?
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Stefan charges $1.25 for gasoline plus $6.50 per hour for mowing lawns. What is x, the number of hours he has to mow lawns to earn more than $50?

Answer 1

To earn a profit of more than $50, Stefan must sell more than
`\( x = 80 \)`cups of lemonade.

Step-by-step explanation:

Stefan's profit can be calculated using the equation
`\( \text{Profit} = \text{Revenue} - \text{Cost} \).`The revenue from selling
`\( x \)`cups of lemonade is
`\( 1.25x \),` and the cost is $6.50. Therefore, the profit equation is
`\( 1.25x - 6.50 \).` To find the number of cups needed to earn a profit of more than $50, set the profit greater than $50 and solve for
`\( x \):`

`\[ 1.25x - 6.50 > 50 \]`

`\[ 1.25x > 56.50 \]`

`\[ x > (56.50)/(1.25) \]`

`\[ x > 45.2 \]`

Since \( x \) represents the number of cups, and cups cannot be in fractions, Stefan needs to sell more than 45 cups to achieve a profit of more than $50. Therefore, the final answer is \( x = 46 \) cups.

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Question 2:

Final Answer:

Stefan needs to deposit
`\( x = 36 \)` weeks with $1.25 each week to have a balance of more than $50 in his savings account.

Step-by-step explanation:

The balance in Stefan's savings account can be expressed by the equation
`\( \text{Balance} = \text{Initial deposit} + \text{Weekly deposit} * \text{Number of weeks} \). In this case, the initial deposit is $6.50,`the weekly deposit is $1.25, and the balance should exceed $50:

`\[ 6.50 + 1.25x > 50 \]`

`\[ 1.25x > 43.50 \]`

`\[ x > (43.50)/(1.25) \]`

`\[ x > 34.8 \]`

Since
`\( x \)` represents the number of weeks, and weeks cannot be in fractions, Stefan needs to deposit for more than 34 weeks to have a balance of more than $50. Therefore, the final answer is
`\( x = 35 \)`weeks.

Answer 2

Answer: 40

Step-by-step explanation:50/1.25