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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