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Mary is 20% older than Sally, and Sally is 40% younger than Danielle.

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Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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New post 25 Mar 2019, 01:07
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (02:46) correct 41% (03:02) wrong based on 39 sessions

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Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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New post 25 Mar 2019, 01:33
Bunuel wrote:
Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


given
m=1.2s
s=0.6D
m+s+d=23.2
solve we get s=6 so m= 7.2
next birthday m = 8
IMO B
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Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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New post 25 Mar 2019, 05:14
Bunuel wrote:
Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


The answer should be B.

Given: \(M=\frac{6}{5}S\) and \(S=\frac{3}{5}D\) and M+S+D=23.2. We are looking for M+1=?

With three equations and 3 formulas, we can plug in and solve.

M+S+D=23.2

\(\frac{6}{5}S\)+S+\(\frac{5}{3}S\)=23.2

Solving for S:
Convert the fractions to a common denominator:

\(\frac{18}{15}S\)+\(\frac{15}{15S}\)+\(\frac{25}{15}S\)=23.2

\(\frac{58}{15}S\)=23.2

S=6

\(M=\frac{6}{5}*6\)

\(M=\frac{36}{5}\)

= 7.2

Therefore, M+1 = 8.2. Answer B.
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Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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New post 25 Mar 2019, 15:49
Bunuel wrote:
Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


\(Mary = 1.2S\)

\(Sally = .6D\)

Rearrange \(S=.6D\) to make.... \(Danielle=\frac{S}{.6}\)

\(M+D+S = 23.2\)

\(1.2S+\frac{S}{.6}+S=23.2\)

\(2.2S+\frac{S}{.6}=23.2\) <--- (multiple each side by .6)

\(1.32S+S=13.92\)

\(2.32S=13.92\)

\(Sally=6\)

\(M=1.2S\)

\(M=1.2(6)\)

\(Mary=7.2\) <--- Current Age
\(Mary=8\) <--- Next Birthday
Answer: B
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Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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New post 27 Mar 2019, 18:58
Bunuel wrote:
Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


We can let Danielle’s age = d, Sally’s age = 0.6d, and Mary’s age = 1.2 x 0.6d = 0.72d.

Since the sum of their ages is 23.2, we have:

d + 0.6d + 0.72d = 23.2

2.32d = 23.2

d = 10

So Mary is 0.72 x 10 = 7.2 years old, so she’ll be 8 on her next birthday.

Answer: B
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Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.   [#permalink] 27 Mar 2019, 18:58
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