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Answered

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At present Mary is four years older than Peter. Peter’s age is five – sixths of Mary’s age.
What are their ages?

Sagot :

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Answer:

Peter is 20 years old and Mary is 24 years old

Step-by-step explanation:

1. Mary is four years older than Peter:

M = P + 4

2. Peter’s age is five-sixths of Mary’s age:

[tex]P = \frac{5}{6}M[/tex]

We can substitute the first equation into the second equation to find the values of ( P ) and ( M ):

[tex]{ \text{Substitute }( M = P + 4 ) \: into \: ( P = \frac{5}{6}M ):}[/tex]

[tex]P = \frac{5}{6}(P + 4)[/tex]

To solve for ( P ), first distribute :

[tex](\frac{5}{6})[/tex]

[tex]P = \frac{5}{6}P + \frac{5}{6} \cdot 4[/tex]

[tex]P = \frac{5}{6}P + \frac{20}{6}[/tex]

[tex]P = \frac{5}{6}P + \frac{10}{3}[/tex]

Next, subtract

[tex](\frac{5}{6}P)[/tex]

from both sides to isolate ( P ):

[tex]P - \frac{5}{6}P = \frac{10}{3}[/tex]

Combine the terms on the left side:

[tex]\frac{1}{6}P = \frac{10}{3}[/tex]

To solve for ( P ), multiply both sides by 6:

[tex]P = 6 \cdot \frac{10}{3}[/tex]

[tex]P = \boxed {20}[/tex]

Now that we know Peter's age (( P = 20 )), we can find Mary's age using ( M = P + 4 ):

[tex]M = 20 + 4[/tex]

[tex]M = \boxed {24}[/tex]

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