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# heightof three brothers

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the sum of the heights of three brothers is 221 inches. A is 8 inches taller than B and 5 inches taller than C. WHat is A's height in inches?

Dec 14, 2018

#1
+4221
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We set up equations. a+b+c=221, a=b+8, a=c+5

Dec 14, 2018
#3
+701
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Substituting into b = a - 8 and c = a - 5 is probably more helpful...

PartialMathematician  Dec 15, 2018
#4
+701
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I don't think you are done with your answer, so I'll just finish it for you.

PartialMathematician  Dec 15, 2018
#2
+701
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We have the equation a+b+c=221, and we understand that \(b = a-8\) and \(c= a-5\). Substituting b and c with their values in terms of a, we have \(a + a - 8 + a - 5 = 221, \), which simplifies into \(3a = 234\). Dividing both sides by 3, we have  \(a = 78\) , so a's height is \(\boxed{78}\) inches.

If you wanted to know the height of b and c, we can revisit the equations b = a - 8 and c = a - 5. Simplifying b = 78 - 8, we know that b is 70 inches tall, and simplifying c = 78 - 5, we know that c is 73 inches tall.

If you want to check your work, we can add 78, 70, and 73 to get 221, so our answers are correct.

Hope this helps,

- PM

Dec 15, 2018
edited by PartialMathematician  Dec 15, 2018