From: "Quandaries and Queries Consultants" Sender: "Janelle gariss" <4byhim@silvernet.net> To: A word problem
  Date: Wed, 24 Mar 1999 13:20:23 -0800

A second number is 4 less than a first number. The product of the second number and 3 more than the first number is 18. Find the pair of numbers.

That is my question

My name is Anna and it is 11th grade math and I am a student

Hi Anna,

There are 3 phases in solving the problem.
 
Phase 1: Translate from English to mathematics.
 
Phase 2: Do the mathematics.
 
Phase 3: Translate back into English.
 
Here is an approach the first translation.
 
Phase 1:
First try to change the words into symbols.
The first sentence tells us that

the second number is 4 less than the first number.

Let f be the first number and s the second number then this sentence says

s is 4 less than f

translate this as

s = f - 4

The second sentence tells us that

the product of the second number and 3 more than the first number is 18

That is

the product of s and 3 more than f is 18

or translated

s(f + 3) = 18

Phase 2:
Since s = f - 4 and s(f + 3) = 18, we get (f - 4)(f + 3) = 18. Moving the 18 to the left side of the equation, expanding and collecting like terms gives a quadratic that you can solve either by factoring or using the general quadratic formula. You will get 2 values for f and each one will give you a value for s since s = f - 4 and so you will have 2 sets of answers.

Phase 3:
Write and English sentence that answers tha question.

I hope that this helps.
Jack and Penny

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