Write an inequality

[jakezepre]

The question: On a vacation to Greece, Sam, Ben, Grayson and Alyssa decide to hire a tour guide. Sam agrees to pay twice as much as Alyssa, and Ben and Grayson agree to pay half as much as Alyssa. The tour guide charges a minimum of $50 for a one-hour tour, and $20 for each additional hour.

Write an inequality expressing Alyssa's cost, C, in terms of the length of the tour H.

I have a test tomorrow and I am very confused on what to do with this word problem. If you can please help because I'm extremely lost.

 

[Loren]

I don't see why you want an inequality. It seems to me you have enough information to write an equation.
Sometimes you can get the idea as to how to attack the problem by plugging in real numbers instead of variables and solving for what is asked.

Suppose they tour for 5 hours. They would owe 50+20(5-1).
If Alyssa's cost is $30, then Sam's cost is 2(30) or 60 and Ben and Grayson each pay (1/2)30.

Now, we can write an equation 30 + 2(30) + (1/2)30 = 50+20(5-1)

Now, we substitute C back into this equation for 30 and H in place of 5 and rearrange the inequality as desired.