Mark is 2 years older than 5 times as his daughter, Ana. The product of his age ...

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September 2022 1 4 Report

Mark is 2 years older than 5 times as his daughter, Ana. The product of his age 2 years ago and Ana's age 2 years from now is . 400. What are their present ages? show your solution po need ko po now

Answers & Comments

Claaang29

Answer:

Mark's Age = 16.19 y/o

His daughter's age = 3.64 y/o

Step-by-step explanation:

Let:

x= mark's age

y=his daughter's age

x+2=5y

(x+2)/5 = y ---> eq. 1

(x-2)(y+2) =400 ----> eq. 2

substitute eq. 1 to eq. 2

$(x - 2)( \frac{x + 2}{5} + 2) = 400 \\ (x - 2)( \frac{x + 2 + 10}{5} ) = 400 \\ (x - 2)( \frac{x + 12}{5}) = 400 \\ {x}^{2} + 12x - 2x - 24 = 400 \\ {x}^{2} + 10x - 424 = 0 \\$

a= 1, b=10, c=-424

$x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ = \frac{ - ( 10) + \sqrt{ {( 10)}^{2} - 4(1)( - 424)} }{2(1)} \\ x = 16.19$

from eq. 1

(16.19 -2)/5 = y

y = 3.638

Therefore,

Mark's is 16.19 years old and his daughter is 3.64 years old.

Questions

Answers & Comments

(x+2)/5 = y ---> eq. 1

(x-2)(y+2) =400 ----> eq. 2

substitute eq. 1 to eq. 2

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