by guest author and test prep expert Jon Siegelman, Ph.D.
Most of my students understand math fairly well. and they certainly understand English. Yet they struggle with word problems. What makes these questions challenging is that they require translating English into math. Here are two ways to help with that challenge:
The first is a tip: first translate, then solve. I often recommend solving problems in small steps, but students who try to translate a little, solve a little, translate some more, etc., usually end up very confused or make a careless error along the way. So you should do all of the translating first, before you solve anything.
The second bit of help is a useful tool that any translator seeks: a dictionary. Instead of translating from English to another language, this dictionary is for translating into math.
For many word problems, you can use this dictionary to translate word-for word.
Q. If 3 more than twice a number is 17, what is the number?
3 + 2x = 17
Q. If 15 percent of a number is 8, what is the number?
15/100 X n = 8
Q. If 5 per cent of 20 percent of a positive number is equal to z percent of 25 percent of the same number, what is the value of z?
5/100 X 20/100 X n = z/100 X 25/100 X n (divide both sides by n and just solve for z)
Note that you can convert the fractions to decimals with your calculator if you wish.
To be sure, not every word problem can be solved solely by translation. But the dictionary can still help.
Q. The price of a camera was first increased by 20 percent and then the new price was decreased by 25 percent. The latest price was what percent of the initial price?
Let p = initial price of the camera
Increased price = p + (20/100 X p) = 1.2p
Final price = 1.2p – (25/100 X 1.2p) = 1.2p – 0.3p = 0.9p, which is 90% of the initial price.
You can make this even easier by plugging in for p. Say p = $100 (often a good value to use on percent problems). After the increase, the camera costs $120, and the 25% decrease means the final price is $90.
Finally, you can combine formulas with the dictionary to solve some problems. For example, if a problem has the words “area of a triangle,” translate them to 0.5bh. You should also know that the formula for average (arithmetic mean) is avg = (sum of a list of values)/(number of values in the list).
Q. If the average of x and 2x is y, and y is 3 more than 5 times z, what is the value of x in terms of z?
Using the average formula, you can translate “the average of x and 2x” into (x + 2x)/2
(x + 2x)/2 = y
So (x + 2x)/2 = 3 + 5z (and solve for x in terms of z).
The dictionary should come in handy on your test, and it’s so short and intuitive that you should be able to memorize it easily.
Dr. Siegelman has worked as a private tutor specializing in test preparation for 35 years, and he has run Scorebusters Tutorial Service in New York for 23 years. You can read Jon’s blog at satdude.wordpress.com
