Let me guess: Ever since you woke up this morning, all you've been able to think about is algebraic equation solving involving money. Am I right? Well, you're in luck! That's exactly what we're going to look at today.
Here's a question:
The cost of renting a car from company A is $850 for up to and including 86 miles and $0.50 per mile thereafter. The cost of renting a car from company B is $3.50 per mile for any amount of miles. For a trip that lasts h miles, the cost of renting from company A is the same as the cost of renting from company B. If h is a positive integer greater than 86, what is the value of h?
The SAT makers love writing math questions that involve money. This isn't so surprising: We all buy things and know how money works. But sometimes things can get a little complicated. For example, you might come across a question that asks you to calculate someone’s salary or how much someone has to pay for a gift, and multiple parts of these questions will be in terms of variables. We'll call these questions variable money problems.
The key to solving variable money problems is to not freak out about the variables. Most of the questions use fairly simple concepts; the test makers are just trying to throw you off by using two, three, or even more variables. Here's an example:
The SAT Math section will include a few questions that require you to work with combinations. A combination is just an unordered grouping of elements (for example, if you have two children, how many gender combinations are there?). But you don't need to get hung up on the category; you just need to figure out what the question is asking for. Let's take a look at an example:
Jeff is choosing a frame for his painting. Frames come in 3 different materials (metal, plastic, and wood) and 4 different colors (gold, silver, bronze, and white). How many different types of frames can Jeff buy?
No, unfortunately this isn’t a post about your favorite old-school Blink-182 song, but it's almost as exciting: We’re going to tackle age-related word problems. These questions present you with some clues about how old one or more people are, and then ask you to figure out someone’s exact age or who’s oldest or something like that. Let’s take a look at a couple of examples:
Johnny is currently 4 times as old as his brother, Sam. In two years, Johnny will only be 3 times as old as Sam. How old was Johnny a year ago?
Those wacky people at College Board sure love a good riddle. Often in the SAT Math sections, you'll come across a word problem asking you to find some number by analzing a given set of clues. To make things even more fun, these questions are often found in the Student-Produced Response section—no multiple choice!
Here's a look at one of the more difficult “number-finding” questions you might find on the SAT:
Continuing with our discussion of tricky word problems, today we’re going to talk about word problems involving motion. Again, the difficulty in these questions lies in digging through the depths of confusing language to find your mathematical equation. Luckily, motion problems will tend to boil down to one simple equation:
The SAT Math section doesn’t simply test your knowledge of formulas and equations. It tests whether you know how to apply that knowledge to a given situation. That’s why the SAT Math section is loaded with all kinds of bizarre word problems. These problems are meant to confuse you, and the key to answering them is to figure out which equation you need to solve. Today, we’re going to take a look at a particularly difficult type of word problem: problems involving work.
Here’s an example of a typical SAT work problem:
Liz and Jack are writing sketches for their sketch comedy show. Liz can write a complete show in 5 hours and Jack can write a complete show in 10 hours. If they work together (and at the same pace as they would individually), how many hours will it take Liz and Jack to write a complete show?
