1Cademy - Solving a Two-Number Problem with Negative Results

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Solving a Two-Number Problem with Negative Results

Apply the seven-step problem-solving strategy to a two-unknown number problem where the given sum is negative and the relationship uses "less than," producing negative solutions. Problem: The sum of two numbers is $-15$ . One number is nine less than the other. Find the numbers. 1. Read the problem. 2. Identify what to find: two numbers. 3. Name the unknowns. Let $n$ = the first number. Because one number is "nine less than" the other, the second number is $n - 9$ . 4. Translate into an equation: The sum of the two numbers is $-15$ , so: $n + (n - 9) = -15$ 5. Solve the equation. Combine like terms: $2n - 9 = -15$ Add $9$ to both sides: $2n = -6$ Divide both sides by $2$ : $n = -3$ Find the second number: $n - 9 = -3 - 9 = -12$ . 6. Check: Is $-12$ nine less than $-3$ ? $-3 - 9 = -12$ $\checkmark$ . Is their sum $-15$ ? $-3 + (-12) = -15$ $\checkmark$ . 7. Answer: The numbers are $-3$ and $-12$ . This example extends the two-unknown number problem pattern to situations involving negative numbers. The phrase "nine less than" translates to subtraction ( $n - 9$ ), and the negative sum means the equation $2n - 9 = -15$ requires adding $9$ rather than subtracting. The verification step is especially important here, because working with negative numbers increases the likelihood of sign errors.

Updated 2026-04-22

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