Question

Vacation Costs - Your family is planning a 7-day vacation in Florida. You estimate that it will cost $275 per day in Tampa and $400 per day in Orlando. Your total budget for the 7-days is $2,300. How many days do you spend in each location? Systems of equations only

Answer 1

3 days in Orlando and 4 days in Tampa

Explanation:

Represent Tampa with T and Orlando with L

Given

`Cost\ in\ T = 275`

`Cost\ in\ L = 400`

`Total = 2300`

`Days = 7`

Required

Solve for T and L

We start by representing the given data, algebraically;

In terms of days:

`T + L = 7`

In terms of cost:

`275T + 400L = 2300`

Make T the subject in (1)

`T = 7 - L`

Substitute in (2)

`275(7 - L) + 400L = 2300`

`1925 - 275L + 400L = 2300`

Collect Like Terms

`- 275L + 400L = 2300 - 1925`

`125L = 375`

Divide through by 125

`L = 375/125`

`L = 3`

Recall that

`T = 7 - L`

`T = 7 - 3`

`T = 4`

This implies 3 days in Orlando and 4 in Tampa