Question

Costs for a campground are $60 for 1 night and $150 for 3 nights. Assuming that the cost increases linearly, which equation shows the cost, c, for n nights?

Answer 1

SOLUTION

GIVEN

Costs for a campground are $ 60 for 1 night and $ 150 for 3 nights.

TO DETERMINE

Assuming that the cost increases linearly, which equation shows the cost, c, for n nights

EVALUATION

Here it is given that cost is $ c for n nights

Since the cost increases linearly

Let the required relation be

$\sf{c = a + nb} \: \: \: - - - (1)$

Now Costs for a campground are $60 for 1 night

We get from equation 1

$\sf{60 = a + b} \: \: \:$

$\sf{ \implies \: a + b = 60} \: \: \: \: \: - - - (2)$

Again $ 150 for 3 nights

We get from equation 1

$\sf{ a +3 b = 150} \: \: \: \: \: - - - (3)$

Equation 3 - Equation 2 gives

2b = 90

$\sf{ \implies \: b = 45 }$

Equation 2 gives

$\sf{ a = 60 - 45 = 15 }$

Equation 1 gives

$\sf{c = 15 + 45n}$

Which is the required linear equation

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