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Problem 3 is a Pre-Algebra word problem that's similar to ACT questions early on the ACT
Math test. Give it a try and then I'll go through the solution.
The correct answer to problem 3 is B. This is a word problem that requires some
basic math. Let's start by marking the important parts:
We have a budget of 65,000 for parking spaces, and the cost of each one is $1055. After the
first 30 have been completed, we want to know how many more can be built while staying within
the budget of 65,000.
Here's one way to think about this: Since we have 65,000 to spend on parking spaces
and they cost 1055 each, a TOTAL of 65,000/1055, or 61.61, spaces can be built.
We can't round up here because if we built 62 spaces, we'd spend more than 65,000 dollars.
Also we're only interested in completed spaces, so the fractional part doesn't do us any good.
We need to take the next LOWER integer: 61. A total of 61 parking spaces can be built.
Now since 30 spaces have already been completed, that leaves 61-30=31 more spaces, choice B.
If you rounded up to 62 spaces, you'd have gotten 32, but this is wrong because the problem
specifically states without going over the budget. If we put in 32 spaces in addition
to the 30 already completed, we'd go over the $65,000 budget by around $400.
There's another approach to solving this problem that you may have used. Since 30 spaces have
been completed, we can calculate how much we've spent like this 30 times 1055 is equal
to 31,650. That's how much of the 65,000 was spent on
the first 30 spaces. So the amount we have left is 65,000-31,650=33,350. Dividing this
by 1055 gives the number of additional spaces we can put in: 33,350/1055=31.61.
And again, since we want completed spaces, we have to take the next lower integer, 31.
Notice that this second approach has a few more calculations so it takes a little more
time. Keep in mind that there're often a couple of different ways to work a problem.
In this problem we mostly just used basic math operations, like multiplication and division.
Here's a reminder about some of the ways these operations show up.
For multiplication we have ab or a dot b or we can use a times symbol which looks like
the letter x. We can also have parenthesis around one or both terms.
For division we can have a over b or the standard division sign or a slash. And we can also
have parenthesis around one or both terms. All of these forms mean exactly the same thing.
One last note, the ACT math test is ordered from easiest to hardest, with the problems
most likely to be answered correctly near the beginning of the test, and the ones most
likely to be missed, toward the end. This practice test is arranged that way too.
That means the problems will become more challenging as you work your way through.