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Likurg_2 [28]
2 years ago
9

Having some trouble with these questions, how do I work them out?

Mathematics
1 answer:
matrenka [14]2 years ago
7 0

5.

Let x be the age of the father and y be the age of the son. As of today, he's 3 times older, so we have x=3y

10 years ago their ages were, respectively, x-10 and y-10, and the father was 5 times older: x-10 = 5(y-10)

So, we have the system

\begin{cases} x=3y\\x-10=5(y-10)\end{cases}

Using the first equation, we can substitute every occurrence of "x" with "3y" in the second equation:

3y-10=5(y-10) \iff 3y-10=5y-50 \iff 2y = 40 \iff y=20

So, the son is 20 years old, which means that the father is 60 years old.

Indeed, 10 years ago they were 10 and 50 years old, so the father was 5 times older.

6.

Let x be the age of the grandfather and y the age of the granddaughter. We know that the grandfather is 10 times older: x=10y

He also is 54 years older: x=y+54

Again, if we substitute x=10y in the second equation we have

10y=y+54 \iff 9y=54 \iff y=6

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______________________

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