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One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.
9, 15
The sum of two numbers is fifty-eight. One number is four more than the other. Find the numbers.
27, 31
The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.
| Step 1. Read the problem. | ||
| Step 2. Identify what we are looking for. | We are looking for two numbers. | |
| Step 3. Name. | ||
| Choose a variable. | Let number. | |
| One number is 4 less than the other. | number | |
| Step 4. Translate. | ||
| Write as one sentence. | The sum of the 2 numbers is negative 14. | |
| Translate into an equation. |
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| Step 5. Solve the equation. |
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| Combine like terms. |
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| Add 4 to each side and simplify. |
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| Simplify. |
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| Step 6. Check. | ||
| Is −9 four less than −5? | ||
| Is their sum −14? | ||
| Step 7. Answer the question. | The numbers are −5 and −9. |
The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.
The sum of two numbers is One number is 40 more than the other. Find the numbers.
One number is ten more than twice another. Their sum is one. Find the numbers.
| Step 1. Read the problem. | ||
| Step 2. Identify what you are looking for. | We are looking for two numbers. | |
| Step 3. Name. | ||
| Choose a variable. | Let number. | |
| One number is 10 more than twice another. | number | |
| Step 4. Translate. | ||
| Restate as one sentence. | Their sum is one. | |
| The sum of the two numbers is 1. | ||
| Translate into an equation. |
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| Step 5. Solve the equation. | ||
| Combine like terms. |
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| Subtract 10 from each side. |
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| Divide each side by 3. |
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| Step 6. Check. | ||
| Is ten more than twice −3 equal to 4? | ||
| Is their sum 1? | ||
| Step 7. Answer the question. | The numbers are −3 and −4. |
One number is eight more than twice another. Their sum is negative four. Find the numbers.
One number is three more than three times another. Their sum is Find the numbers.
Some number problems involve consecutive integers. Consecutive integers are integers that immediately follow each other. Examples of consecutive integers are:
Notice that each number is one more than the number preceding it. So if we define the first integer as n , the next consecutive integer is The one after that is one more than so it is which is
The sum of two consecutive integers is 47. Find the numbers.
| Step 1. Read the problem. | ||
| Step 2. Identify what you are looking for. | two consecutive integers | |
| Step 3. Name each number. | Let integer. | |
| next consecutive integer | ||
| Step 4. Translate. | ||
| Restate as one sentence. | The sum of the integers is 47. | |
| Translate into an equation. |
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| Step 5. Solve the equation. |
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| Combine like terms. |
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| Subtract 1 from each side. |
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| Divide each side by 2. |
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| Step 6. Check. | ||
| Step 7. Answer the question. | The two consecutive integers are 23 and 24. |
The sum of two consecutive integers is Find the numbers.
47, 48
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