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# In 1950 Roberto was four times as old as Juan. In 1955, Robe

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In 1950 Roberto was four times as old as Juan. In 1955, Robe [#permalink]  22 May 2017, 01:15
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In 1950 Roberto was four times as old as Juan. In 1955, Roberto was three times as old as Juan. How old was Roberto when Juan was born?

A) 5

B) 10

C) 20

D) 30

E) 40
[Reveal] Spoiler: OA

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Re: In 1950 Roberto was four times as old as Juan. In 1955, Robe [#permalink]  22 May 2017, 08:49
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Carcass wrote:

In 1950 Roberto was four times as old as Juan. In 1955, Roberto was three times as old as Juan. How old was Roberto when Juan was born?

A) 5

B) 10

C) 20

D) 30

E) 40

In 1950 Roberto was four times as old as Juan.
Let J = Juan's age in 1950
So, 4J = Roberto's age in 1950

In 1955....
IMPORTANT: Before we use the information about Roberto being three times as old as Juan, let's first determine the algebraic representation of each person's age
If J = Juan's age in 1950, then J+5 = Juan's age in 1955
If 4J = Roberto's age in 1950, then 4J+5 = Roberto's age in 1955

.... Roberto was three times as old as Juan.
So, we have two ages (in 1955)
J+5 = Juan's age
4J+5 = Roberto's age
Are these two ages equal?
No. Roberto's age is three times Juan's age
In other words, 4J+5 = 3(J+5)
Expand to get: 4J + 5 = 3J + 15
Solve: J = 10

Since J = Juan's age in 1950, we now know that Juan was 10 years old in 1950
Since 4J = Roberto's age in 1950, we now know that Roberto was 40 years old in 1950

How old was Roberto when Juan was born?
This is a cute way to ask "Roberto is how many years older than Juan?"
Well, in 1950, Roberto was 30 years older than Juan. So, if we assume they age at the same rate ( ), then the correct answer is D

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Re: In 1950 Roberto was four times as old as Juan. In 1955, Robe [#permalink]  20 Mar 2018, 02:47
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Now this is a classic example of a question that I will end up getting wrong because I am in such a hurry to chose the answer without fully reading the question
Carcass wrote:

In 1950 Roberto was four times as old as Juan. In 1955, Roberto was three times as old as Juan. How old was Roberto when Juan was born?

A) 5

B) 10

C) 20

D) 30

E) 40
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Posts: 16
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Re: In 1950 Roberto was four times as old as Juan. In 1955, Robe [#permalink]  04 Aug 2019, 14:48
Really good question!!!
Re: In 1950 Roberto was four times as old as Juan. In 1955, Robe   [#permalink] 04 Aug 2019, 14:48
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