Use a Problem Solving Strategy: example 9.7

The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

The sum of two numbers is negative twenty-three. One number is $7$ less than the other. Find the numbers.

How did it go?

Step 1. Read the problem.
Step 2. Identify what you are looking for.		two numbers
Step 3. Name. Choose a variable. What do you know about the second number? Translate.		Let n = 1^st number One number is 4 less than the other. n - 4 = 2^nd number
Step 4. Translate. Write as one sentence. Translate into an equation. Substitute the variable expressions.		The sum of two numbers is negative fourteen.
Step 5. Solve the equation.
Combine like terms.
Add 4 to each side and simplify.
Divide by 2.
Substitute $n = −5$ to find the 2^nd number.


Step 6. Check:
Is −9 four less than −5? Is their sum −14?
Step 7. Answer the question.		The numbers are −5 and −9.

Step 1. Read the problem.
Step 2. Identify what you are looking for.		two numbers
Step 3. Name. Choose a variable. What do you know about the second number? Translate.		Let n = 1^st number One number is 4 less than the other. n - 4 = 2^nd number
Step 4. Translate. Write as one sentence. Translate into an equation. Substitute the variable expressions.		The sum of two numbers is negative fourteen.
Step 5. Solve the equation.
Combine like terms.
Add 4 to each side and simplify.
Divide by 2.
Substitute $n = −5$ to find the 2^nd number.


Step 6. Check:
Is −9 four less than −5? Is their sum −14?
Step 7. Answer the question.		The numbers are −5 and −9.