Answer:
David is 55 years old
Morgan is 23 years old
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Step-by-step explanation:
Let the age of David = x years
Let the age of Morgan = y years
<u>We are Given:</u>
The sum of David and Morgan's age is 78
7 years ago, David's age was 3 times Morgan's age
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<u>Making the equations:</u>
from the first statement, the sum of their ages is 78
So, we can write it as:
x + y = 78
from the second statement,7 years ago, David's age was 3 times Morgan's age
David's age 7 years ago = (x - 7)
Morgan's age 7 years ago = (y-7)
So, we can write the equation as:
(x - 7) = 3(y - 7)
which can be simplified to:
x = 3y - 14
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<u>Solving the equations:</u>
We have the 2 equations:
from the first equation, we can say that:
x = 78 - y
Using this value in the second equation:
x = 3y - 14
78 - y= 3y - 14 [<em>since x = 78 - y</em>]
78 + 14 = 4y
4y = 92
y = 23
Using this value in the first equation:
x + y = 78
x + 23 = 78 [<em>since y = 23</em>]
x = 55
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<u>The Age of David and Morgan:</u>
Since we assigned x to the age of David:
David is 55 years old
We assigned y to the age of Morgan. So,
Morgan is 23 years old
