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Translate to a system of equations:
A couple has a total household income of $84,000. The husband earns $18,000 less than twice what the wife earns. How much does the wife earn?
Translate to a system of equations:
A senior employee makes $5 less than twice what a new employee makes per hour. Together they make $43 per hour. How much does each employee make per hour?
We set up, but did not solve, the systems of equations in [link] and [link] Now we’ll translate a situation to a system of equations and then solve it.
Translate to a system of equations and then solve:
Devon is 26 years older than his son Cooper. The sum of their ages is 50. Find their ages.
| Step 1. Read the problem. | |
| Step 2. Identify what we are looking for. | We are looking for the ages of Devon and Cooper. |
| Step 3. Name what we are looking for. | Let
Devon’s age.
Cooper’s age |
| Step 4. Translate into a system of equations. | Devon is 26 years older than Cooper. |
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| The sum of their ages is 50. | |
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| The system is: |
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Step 5. Solve the system of equations.
Solve by substitution. |
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| Substitute c + 26 into the second equation. |
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| Solve for c . |
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| Substitute c = 12 into the first equation and then solve for d . |
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| Step 6. Check the answer in the problem. | Is Devon’s age 26 more than Cooper’s?
Yes, 38 is 26 more than 12. Is the sum of their ages 50? Yes, 38 plus 12 is 50. |
| Step 7. Answer the question. | Devon is 38 and Cooper is 12 years old. |
Translate to a system of equations and then solve:
Ali is 12 years older than his youngest sister, Jameela. The sum of their ages is 40. Find their ages.
Ali is 28 and Jameela is 16.
Translate to a system of equations and then solve:
Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42. Find their ages.
Jake is 9 and his dad is 33.
Translate to a system of equations and then solve:
When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for 20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes on the elliptical trainer and 30 minutes circuit training she burned 473 calories. How many calories does she burn for each minute on the elliptical trainer? How many calories does she burn for each minute of circuit training?
| Step 1. Read the problem. | |
| Step 2. Identify what we are looking for. | We are looking for the number of
calories burned each minute on the elliptical trainer and each minute of circuit training. |
| Step 3. Name what we are looking for. | Let
number of calories burned per minute on the elliptical trainer.
number of calories burned per minute while circuit training |
| Step 4. Translate into a system of equations. | 10 minutes on the elliptical and circuit
training for 20 minutes, burned 278 calories |
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| 20 minutes on the elliptical and
30 minutes of circuit training burned 473 calories | |
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| The system is: |
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| Step 5. Solve the system of equations. | |
| Multiply the first equation by −2 to get opposite coefficients of e . |
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| Simplify and add the equations.
Solve for c . |
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| Substitute c = 8.3 into one of the original equations to solve for e . |
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| Step 6. Check the answer in the problem. | Check the math on your own. |
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| Step 7. Answer the question. | Jenna burns 8.3 calories per minute
circuit training and 11.2 calories per minute while on the elliptical trainer. |
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