Question

In the equations, A and B represent the price per night for a room in Hotel A and Hotel B, respectively, w weeks after September 1 last autumn. What was the price per night in Hotel A when it was equal to the price per night in Hotel B? A = 240 − 20w B = 320 − 30w

Answer 1

the answer is A 80

i just did it on usatestprep

Answer 2

A = B = 80 . . . per night

Explanation:

The value of w that makes the prices equal can be found from ...

A = B

240 -20w = 320 -30w

10w = 80

Substituting this value into the equation for A, we get ...

A = 240 -2(10w) = 240 -2(80) = 80

We can check that we also get the same value for B:

B = 320 -3(10w) = 320 -3(80) = 80

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Comment on this solution

We could go to the trouble to divide by 10 to find w=8, but then we would need to multiply it by 10 again to get 20w or 30w. We can just use the result as is without the extra steps.