SOLUTION: Derrick is 5 less than twice as old as Brandon. The sum of their ages is 43. How old are Derrick and Brandon?

Question 620610: Derrick is 5 less than twice as old as Brandon. The sum of their ages is 43. How old are Derrick and Brandon?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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STEP I: Set your variables.
Let d be Derrick's age.
Let b be Brandon's age.
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STEP II: Use information in the problem to write equations that model the situation.
In algebra, the phrase "Derrick is 5 less than twice as old as Brandon" can be written as,

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"The sum of their ages is 43" can be written as,

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STEP III: Solve the system of two equations with two variables.
Substitute 2b-5 for d in the second equation.

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Simplify by combining like terms and solve for b.

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The equation b=16 means that Brandon is 16 years old.
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Substitute 16 for b in either equation. I'll use the second.

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Solve for d.

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The equation d=27 means that Derrick is 27 years old.
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STEP IV: Check your work by checking your answers in the original problem.
Is Derrick 5 less than twice a old as Bandon? Twice 16 is 32, and 27 is 5 less than 32. Check!
Is the sum of their ages 43? 16+27=43. Check!!!
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Hope this helps! Feel free to email if you have questions about this solution.
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MsFiggy
math.in.the.vortex@gmail.com
Derrick is 5 less than twice as old as Brandon. The sum of their ages is 43. How old are Derrick and Brandon?
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