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Difference between revisions of "2000 AMC 8 Problems/Problem 10"

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Shea grows 20%, so she was originally 60/1.2=50 inches tall which is a 10 inch increase. Since Ara grew half as much as Shea, Ara grew 5 inches therefore Ara is now 50+5=55 inches tall which is choice E.
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==Problem==
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Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?
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<math>\text{(A)}\ 48 \qquad \text{(B)}\ 51 \qquad \text{(C)}\ 52 \qquad \text{(D)}\ 54 \qquad \text{(E)}\ 55</math>
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==Solution==
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Shea has grown <math>20\%</math>, if x was her original height, then <math>1.2x = 60</math>, so she was originally <math>\frac{60}{1.2}=50</math> inches tall which is a <math>60 - 50 = 10</math> inch increase. Ara also started off at <math>50</math> inches.  Since Ara grew half as much as Shea, Ara grew <math>\frac{10}{2} = 5</math> inches.  Therefore, Ara is now <math>50+5=55</math> inches tall which is choice <math>\boxed{E}.</math>
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==See Also==
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{{AMC8 box|year=2000|num-b=9|num-a=11}}
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{{MAA Notice}}

Latest revision as of 23:27, 7 January 2020

Problem

Ara and Shea were once the same height. Since then Shea has grown 20% while Ara has grown half as many inches as Shea. Shea is now 60 inches tall. How tall, in inches, is Ara now?

$\text{(A)}\ 48 \qquad \text{(B)}\ 51 \qquad \text{(C)}\ 52 \qquad \text{(D)}\ 54 \qquad \text{(E)}\ 55$

Solution

Shea has grown $20\%$, if x was her original height, then $1.2x = 60$, so she was originally $\frac{60}{1.2}=50$ inches tall which is a $60 - 50 = 10$ inch increase. Ara also started off at $50$ inches. Since Ara grew half as much as Shea, Ara grew $\frac{10}{2} = 5$ inches. Therefore, Ara is now $50+5=55$ inches tall which is choice $\boxed{E}.$

See Also

2000 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 9 		Followed by
Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

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