Question 874582

Norman is 4 times as old his brother Nicholas. Their combined age is 15. How old is each boy? 

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Step 1.) Label


Let Norman: N (Note: Norman is capital N)


Let Nicholas: n (Note: Nicholas is lower case n)


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Step 2.) Look for keywords.

Norman is(=) 4 times(4x) as old his brother Nicholas(n). 

Their combined(+) age is(=) 15. 


Norman={{{4*n}}}

Nicholas=n

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Step 3.) Using the information we got in step 2, set up the equation.


{{{(4*n)+n=15}}}


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Step 4.) Solve for "n" (Nicholas's age)


{{{(4*n)+n=15}}}

{{{4n+n=15}}}

{{{5n=15}}}

{{{5n/5=15/5}}}

{{{n=3}}}

Nicholas is 3 years old.

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Step 5.) Now that we know Nicholas's age, we can find Norman's age.


Using the answer in step 4) we know n=3


In step 2) we found out that Norman's age is:  N={{{4*n}}}


So now plug in n=3 into the equation to solve for Norman's age.


N={{{4*n}}}


N={{{4*(3)}}}


N=12


Norman is 12 years old.


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Step 6.) Check. 


Remember, 


Let Norman: N (Note: Norman is capital N)



Let Nicholas: n (Note: Nicholas is lower case n)


{{{N+n=15}}}


{{{12+3=15}}}


{{{15=15}}}


Checks!

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Step 7.) Answer.


Norman is 12 years old and Nicholas is 3 years old.