A car rental company charges $100 for the first 50 miles and $10 for every additional 10 miles. If Gregg traveled 150 miles, how much would he pay?

I know the answer intuitively is $200, but how do I set up this equation

100 + 10(150 - 50)

To set up the equation, you need to identify the number of additional miles Gregg traveled beyond the initial 50 miles. Let's denote this as 'x.'

For the first 50 miles, he is charged a fixed rate of $100.

For the additional miles (x), he is charged $10 for every 10 miles.

Since each additional 10 miles incurs an additional charge of $10, we can calculate the number of additional 10-mile increments by dividing x by 10: (x/10).

Now, we can express Gregg's total cost in terms of x:

Total cost = Fixed rate + Additional charges
Total cost = $100 + ($10 * (x/10))

Simplifying, we obtain:

Total cost = $100 + $10 * x/10

The 'x/10' in this case is equivalent to 'x' since dividing by 10 and multiplying by 10 will cancel each other out. Therefore, we can simplify further:

Total cost = $100 + $10 * x
Total cost = $100 + $10x

To determine how much Gregg would pay for traveling 150 miles, substitute x = 150 into the equation:

Total cost = $100 + $10 * 150 = $100 + $1500 = $1600

Therefore, Gregg would pay $1600 for traveling 150 miles.