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This table shows the seasonal revenue and expenses of Whispering Willows Campground over the last year.Campground FinancialsSeason Revenue ExpensesSpring $33,000 $21,100Summer $72,400 $54,700Fall $41,600 $29,100Winter $14,500 $21,100Mrs. Woods manages the campground. She found that the annual revenue and annual expenses were approximately unchanged from year to year. Mrs. Woods wants to write an equation using the variable x to figure out how many years it will take for the campground's all-time total revenue to be $200,000 more than its all-time total expenses.How should Mrs. Woods define the variable x?x = annual revenuex = monthly expensesx = the year the campground openedx = number of years since the campground openedWhich equation can Mrs. Woods use to find how many years it will take for the campground's all-time total revenue to be $200,000 more than its all-time total expenses?(147,000–104,900)x=200,000161,500x+200,000=126,000x(126,000+200,000)x=161,500x126,000x+200,000=161,500xSubmit

Question

This table shows the seasonal revenue and expenses of Whispering Willows Campground over the last year.Campground FinancialsSeason Revenue ExpensesSpring 33,00033,000 21,100Summer 72,40072,400 54,700Fall 41,60041,600 29,100Winter 14,50014,500 21,100Mrs. Woods manages the campground. She found that the annual revenue and annual expenses were approximately unchanged from year to year. Mrs. Woods wants to write an equation using the variable x to figure out how many years it will take for the campground's all-time total revenue to be 200,000morethanitsall−timetotalexpenses.HowshouldMrs.Woodsdefinethevariablex?x=annualrevenuex=monthlyexpensesx=theyearthecampgroundopenedx=numberofyearssincethecampgroundopenedWhichequationcanMrs.Woodsusetofindhowmanyyearsitwilltakeforthecampground′sall−timetotalrevenuetobe200,000 more than its all-time total expenses.How should Mrs. Woods define the variable x?x = annual revenuex = monthly expensesx = the year the campground openedx = number of years since the campground openedWhich equation can Mrs. Woods use to find how many years it will take for the campground's all-time total revenue to be 200,000 more than its all-time total expenses?(147,000–104,900)x=200,000161,500x+200,000=126,000x(126,000+200,000)x=161,500x126,000x+200,000=161,500xSubmit

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Solution

Mrs. Woods should define the variable x as the number of years since the campground opened.

The equation Mrs. Woods can use to find how many years it will take for the campground's all-time total revenue to be $200,000 more than its all-time total expenses is (147,000–104,900)x=200,000.

Here's how to derive this:

  1. First, calculate the total annual revenue and expenses. From the table, we can see that the total revenue for the year is 33,000(spring)+33,000 (spring) + 72,400 (summer) + 41,600(fall)+41,600 (fall) + 14,500 (winter) = 161,500.Thetotalexpensesfortheyearare161,500. The total expenses for the year are 21,100 (spring) + 54,700(summer)+54,700 (summer) + 29,100 (fall) + 21,100(winter)=21,100 (winter) = 126,000.

  2. Since Mrs. Woods found that the annual revenue and annual expenses were approximately unchanged from year to year, we can use these totals in our equation.

  3. We want to find out when the total revenue will be 200,000morethanthetotalexpenses.Thismeansthatthedifferencebetweenthetotalrevenueandtotalexpenses,multipliedbythenumberofyears,shouldbeequalto200,000 more than the total expenses. This means that the difference between the total revenue and total expenses, multiplied by the number of years, should be equal to 200,000.

  4. Therefore, the equation becomes (Total Revenue - Total Expenses) * x = 200,000,whichsimplifiesto(161,500−126,000)∗x=200,000, which simplifies to (161,500 - 126,000) * x = 200,000 or (35,500) * x = $200,000.

  5. So, the final equation is 35,500x = 200,000.

This problem has been solved

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