Use a Problem Solving Strategy: example 9.8

One number is ten more than twice another. Their sum is one. 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.

One number is eight more than twice another. Their sum is negative four. 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. One number is ten more than twice another.		Let x = 1^st number 2x + 10 = 2^nd number
Step 4. Translate. Restate as one sentence.		Their sum is one.
Translate into an equation
Step 5. Solve the equation.
Combine like terms.
Subtract 10 from each side.
Divide each side by 3 to get the first number.
Substitute to get the second number.


Step 6. Check.
Is 4 ten more than twice −3? Is their sum 1?
Step 7. Answer the question.		The numbers are −3 and 4.

Step 1. Read the problem.
Step 2. Identify what you are looking for.		two numbers
Step 3. Name. Choose a variable. One number is ten more than twice another.		Let x = 1^st number 2x + 10 = 2^nd number
Step 4. Translate. Restate as one sentence.		Their sum is one.
Translate into an equation
Step 5. Solve the equation.
Combine like terms.
Subtract 10 from each side.
Divide each side by 3 to get the first number.
Substitute to get the second number.


Step 6. Check.
Is 4 ten more than twice −3? Is their sum 1?
Step 7. Answer the question.		The numbers are −3 and 4.