To set up the equation for your budget, we first need to determine how much money you will use for snacks over the duration of the trip. You mentioned that you budget $25 per day for snacks, and the trip lasts for a week (7 days).
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Calculate the total amount of money spent on snacks over the week: \[ \text{Total snacks cost} = 25 \text{ (per day)} \times 7 \text{ (days)} = 175 \]
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To find the amount of spending money left after the snacks, you start with your total budget, which is $314 and subtract the total cost of snacks: \[ \text{Money left (y)} = 314 - \text{(Total cost of snacks)} \]
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To form a linear equation in terms of days (x), let's express this general formula for any number of days (x): \[ \text{Total cost of snacks for } x \text{ days} = 25x \] Thus, the equation for the amount of spending money left after spending on snacks for \( x \) days is: \[ y = 314 - 25x \]
So, to fill in the blanks in your original equation: \[ y = -25x + 314 \]
Therefore, the linear equation representing the amount of spending money left (y) based on the number of days (x) is: \[ y = -25x + 314 \]