Question
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Yoli lives in New York City and currently spends \( \$ 50 / \) day on variable expenses and \( \$ 3650 / \mathrm{month} \) on fixed expenses. Write an equation that models Yoli's total monthly expenses based on how many day have passed since the beginning of the month.

Ask by Harper Warren. in the United States
Mar 11,2025

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Tutor-Verified Answer

Answer

Yoli's total monthly expenses can be modeled by the equation \( E(d) = 3650 + 50d \), where \( d \) is the number of days since the beginning of the month.

Solution

Let \( d \) represent the number of days that have passed since the beginning of the month. 1. Yoli’s variable expenses per day are \( \$50 \). After \( d \) days, her total variable expenses will be: \[ 50d \] 2. Her fixed monthly expenses remain constant at: \[ 3650 \] 3. Therefore, the equation that models Yoli's total monthly expenses is: \[ E(d) = 3650 + 50d \]

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To model Yoli's total monthly expenses, we can let \( x \) represent the number of days that have passed since the beginning of the month. Her variable expenses, which are \( \$50 \) per day, would amount to \( 50x \). Since her fixed expenses are \( \$3650 \) per month, we can express her total monthly expenses with the equation: \[ \text{Total Expenses} = 3650 + 50x \] This equation effectively combines her fixed and variable expenses based on the number of days that have passed. Now, let's talk about what happens as the month progresses! As each day ticks by, Yoli's variable expenses increase by \( \$50 \), so you can see how quickly costs can add up. This is a handy reminder that keeping track of daily expenses is crucial when managing budgets. On the other hand, having a fixed expense of \( \$3650 \) means Yoli has a reliable baseline for her monthly spending. If she spends more than her fixed amount in variable expenses, she may need to adjust elsewhere to avoid overspending. It's always a balancing act in the wild world of personal finance!

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