# Taking the Headache Out of Word Problems

**This is a guest post by Danielle**

For many math students, word problems are a cause for anxiety and stress. After all, how can you solve a math problem that is written in words, with few numbers to rely on? In my college trigonometry class, I was guilty of this, feeling like an imbecile as I struggled over the most basic of problems. However, what many don’t realize is that all of the numbers you need are contained in the puzzle; you simply have to know how to recognize and implement those numbers in order to find your solution.

The best way to do this is to draw a sketch of the scenario laid out in the puzzle—in essence to illustrate the story being told—in order to solve the problem. Below are three story problems and a step-by-step guide for finding their solutions:

First, an easy one: Sir Patrick and his page Jake could travel **12** miles in **1** day. They were travelling from Gaul heading back to Rome, which is **600** miles away. A big flood flooded their path so they had to wait **4** days for conditions to improve before they could continue. A band of outlaws attacked them and stopped their travels for another **2** days. How many days did it take them in all to get from Gaul to Rome? (I have taken the liberty of emphasizing all of the numbers needed to solve this problem.)

Once you have a basic diagram, you can see that this is far easier than originally anticipated!

First, how many days would the trip have taken, were it not for the delays?

600 ÷ 12 = 50 days

How many days tacked on due to unbelievably bad luck and lack of modern amenities? 6

50 + 6 = 56 days total for trip.

As you can see, once you are able to select the pertinent information from the puzzle and plug them into the right spots, even the most confusingly worded problem becomes easy.

How about one that’s a little more challenging?

**Two** bowls and **three** plates cost $**1421**. The cost of the plate is **half** the cost of the bowl. What is the cost of the bowl?

OO – 2 bowls + ||| – 3 plates = $1421

| = ½ O cost of O = x

½ x + ½x + ½x + x + x = 1421

3.5x=1421

1421 ÷ 3.5 = $406 (cost of bowl)

406 ÷ 2 = $203 (cost of plate)

Easy-peasy.

Now, for a doozie: A fireman rests his ladder against a building, making a **57**? angle with the ground. The bottom of the ladder is **28** feet from the base of the building. How long is the ladder? (For this, I confess that I have already forgotten my trig, so I will be quoting from the website where this problem was originally posted.)

|\

| \

| \ ßx

| \

| \ ß57

28

According to Math with Larry, “The first thing to determine is what trig ratio we should use to solve this problem. We have an angle, we have an adjacent side to that angle, and we need to know the hypotenuse. Referring to SOH-CAH-TOA, we can see that the cosine will help us. We know that cos 57 = 28/x. Using a calculator, we can determine that cos 57 = 0.545 (rounded). Using basic algebra, it is easy to determine that x = 51.4 (rounded). That means that the ladder is 51.4 ft long.”

As you can see, with the proper illustrations, you can simplify any problem, thus relieving your math anxieties and lessening your chances for panic attacks or breaking down into tears during trig quizzes (as I have been known to do). Good luck!

BIO: Danielle realized early in life that she was not a mathematician, and as such is studying business litigation. However, she has learned the importance of a basic understanding of math and its application to real-world problems. Whether she’s looking for sales and using coupons to save money, or figuring out the height of a building for whatever obscure reason she would need to do so, understanding how to interpret numbers plays a vital role in her life.