Some of the tools that I teach my students are
- Answer the question that is asked, not another one.
- Be familiar with the vocabulary.
- When a multiple-choice asks you to supply the value of a variable, try each value in turn.
- Give names to unknown quantities.
Two investors receive a total profit of $14,000. They split the money in a ratio of 4 : 1. How much is the smaller share worth?
b. $ 6,000
c. $ 5,600
d. $ 2,800
e. $ 2,000
We always start by asking the three Who, What, What questions and proceeding from there.
- Who are the main characters? Two people's money, x and y (Tool 4)
- What do we know about them? x and y are in a ratio (Tool 2) of 4 : 1 and they total $14,000
- What does the problem ask? What is the smaller amount?
a. y = 11,200
x / 11,200 = 4 / 1; x = 44,800. x and y add up to 56,000: too large.
Continuing with the other four choices, we see the correct answer is d. $2,800.
There are no words that are a substitute for a student thinking through this process.