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16 Sep 2014, 00:20
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This year, the combined age of the Perkins family members is 78 years. The family consists of four members: a husband, a wife, a daughter, and a son. The husband is 4 years older than the wife. The daughter is 2 years older than the son. If the husband's age is 7 times that of the son, how old is the daughter?
A. 5
B. 7
C. 10
D. 13
E. 14
A. 5
B. 7
C. 10
D. 13
E. 14
16 Sep 2014, 00:20
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Official Solution:
This year, the combined age of the Perkins family members is 78 years. The family consists of four members: a husband, a wife, a daughter, and a son. The husband is 4 years older than the wife. The daughter is 2 years older than the son. If the husband's age is 7 times that of the son, how old is the daughter?
A. 5
B. 7
C. 10
D. 13
E. 14
The plug-in method is the most efficient approach for this question.
Let's start with answer choice C:
If the daughter is 10 years old, then: the son is \(10-2=8\) years old. This means the husband is \(7*8=56\) years old, and the wife is \(56-4=52\) years old. Their combined age is \(10+8+56+52=126\), which is greater than 78. Thus, the daughter's age must be less than 10 years. We can also eliminate choices D and E.
Now, let's consider answer choice B:
If the daughter is 7 years old, then: the son is \(7-2=5\) years old. This implies the husband is \(7*5=35\) years old, and the wife is \(35-4=31\) years old. Their total age comes to \(7+5+35+31=78\). This matches the given sum, so it's the correct answer.
Answer: B
This year, the combined age of the Perkins family members is 78 years. The family consists of four members: a husband, a wife, a daughter, and a son. The husband is 4 years older than the wife. The daughter is 2 years older than the son. If the husband's age is 7 times that of the son, how old is the daughter?
A. 5
B. 7
C. 10
D. 13
E. 14
The plug-in method is the most efficient approach for this question.
Let's start with answer choice C:
If the daughter is 10 years old, then: the son is \(10-2=8\) years old. This means the husband is \(7*8=56\) years old, and the wife is \(56-4=52\) years old. Their combined age is \(10+8+56+52=126\), which is greater than 78. Thus, the daughter's age must be less than 10 years. We can also eliminate choices D and E.
Now, let's consider answer choice B:
If the daughter is 7 years old, then: the son is \(7-2=5\) years old. This implies the husband is \(7*5=35\) years old, and the wife is \(35-4=31\) years old. Their total age comes to \(7+5+35+31=78\). This matches the given sum, so it's the correct answer.
Answer: B
16 Jun 2015, 23:14
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Algebraic approach:
h+w+d+s = 78 (Q: d=?)
h=w+4 => w =7d-18
d=s+2 => s=d-2
h=7s => h=7(d-2)
=> 7d-14+7d-18+d+d-2 = 78
=> 16d = 112
=> d=7
Is it right?
h+w+d+s = 78 (Q: d=?)
h=w+4 => w =7d-18
d=s+2 => s=d-2
h=7s => h=7(d-2)
=> 7d-14+7d-18+d+d-2 = 78
=> 16d = 112
=> d=7
Is it right?
