### Video Transcript

Matthew needs to buy some
clothes. The store’s parking lot has the
shown sign outside. Parking: the first hour is free, one
dollar 50 per hour after that. Write an inequality for 𝑡, the
time in hours, that Matthew can park if he only has eight dollars 25 in
cash. Given that you must pay for
whole hours of parking, use your inequality to find the maximum time that
Matthew can park.

Let’s consider the information
given on the sign. We’re told that the first hour
of parking is free, and the amount of time parked in hours is 𝑡. Every hour after that costs one
dollar 50. So, we might’ve seen that we
need to multiply one dollar 50 by 𝑡. However, as that first hour is
free, we need to multiply one dollar 50 or 1.5 by 𝑡 minus one. We know that parking for two
hours would only cost one dollar 50. And substituting two into this
expression gives us one dollar 50. Likewise, three hours of
parking would cost three dollars as the first hour is free. Substituting three into the
expression gives us three minus one, which is two, and multiplying this by 1.5
gives us three dollars.

Matthew only has eight dollars
and 25 cents in cash. Therefore, this expression
needs to be less than or equal to 8.25. We could distribute the
parentheses on the left-hand side. However, there is no need at
this time. The inequality in terms of 𝑡
is 1.5 multiplies by 𝑡 minus one is less than or equal to 8.25. The second part of this
question asks us to solve the inequality to find the maximum time that Matthew
can park. We can solve the inequality
using inverse operations.

Our first step is to divide
both sides by 1.5. The left-hand side of the
inequality becomes 𝑡 minus one. 8.25 divided by 1.5 is 5.5. Therefore, 𝑡 minus one is less
than or equal to 5.5. Our second and final step is to
add one to both sides of the new inequality. This gives us 𝑡 is less than
or equal to 6.5. We’re told that you must pay
for whole hours of parking. Therefore, 𝑡 must be an
integer. As 𝑡 must be less than or
equal to 6.5, the greatest integer value it can take is six. This means that the maximum
time that Matthew can park for is six hours.