It’s okay to admit it: most everyone loves ACT
math word problems.
There are few things in life more satisfying
than carefully reading through a word problem, defining your variables, putting
together a plan, checking your units, and finally solving. Not to mention the
joys of learning new and useful applications of your math knowledge to real-world
situations, like estimating the height of a tree based on the length of its
shadow or calculating the odds of pulling that red sock from your sock drawer
filled with blue and green socks.
But what if you’re one of those rare unfortunates
who struggle with these problems? Are you condemned to permanently wander the
wastelands with the other math illiterates? In short: no. Follow these simple
steps to rejoin your word-problem-solving friends and neighbors:
1) Expect to read any word
problem twice. All word problems
are designed to confuse you by front loading details, hoping that you’ll try to
hold everything in your head as you read the actual question.
2) Focus on understanding
the question on your first pass through. What
are you solving for? What are the units? Putting these questions in your
own words (and not just repeating the last sentence of the problem) can be
extremely helpful in focusing you on what you need to solve for.
3) Scan the answer
choices. A few may immediately
appear as extremely unlikely and can be eliminated from consideration. The
remaining choices will give you an idea of the range your answer will fall
4) Read again, but for
details. This is where the
majority of your thinking and solving will happen, so take your time here.
Isolate the relevant numbers and try to organize your thoughts graphically.
Very few higher difficulty word problems can be solved in your head, so get
everything written out and organized.
5) Solve and bask in the glow of your own brilliance for ONE second, and
then move on to the next question!
Let’s walk through an example:
Parking a car at a short-term airport parking lot costs $2.50
for the 1st hour or any part thereof, $2.25 for the 2nd hour or any part
thereof, and $1.75 for each additional hour or any part thereof after the 2nd
hour. Your ticket shows that you parked your car in this lot from 9:38 a.m. to 2:17
p.m. on the same day. What is the cost of parking your car in the short-term
airport parking lot, according to this ticket?
include all applicable sales tax.)
- Note how many different details are presented to you in this problem. There’s the different prices for each hour and also the length of time the car is parked.
- The question itself is straightforward: “What is the cost?” Solving that question involves figuring out a dollar amount that accounts for the time spent parked in the lot.
- The answer choices are fairly close, ranging from $10.00 to $13.50, so we’re probably not going to be able to eliminate any choices at this point.
- Returning to the details, we know we need to work out timing first, since the price per hour is dependent on how much time we’ve spent in the garage. Parking from 9:38 a.m. to 2:17 p.m. means we were parked in the garage for a little under six hours. To be precise, 5 hours and 39 minutes. The phrase “any part thereof” means that anything over the previous hour counts as another hour. So we’re looking at paying for 6 hours of parking.
- That means we were there for the first hour, the second hour and then four more hours. Going back to our hourly rate, that would mean 2.50+2.25+4(1.75) = 11.75. So our correct answer choices must be A.
That’s all there is to it! Practice your newfound word problem solving expertise on the problems below.