The sum of the ages of David and Morgan is 78 years. 7 years ago, David's age was 3 times Morgan's age. How old is David now?

David is 55 years old

Morgan is 23 years old

Step-by-step explanation:

Let the age of David = x years

Let the age of Morgan = y years

We are Given:

The sum of David and Morgan's age is 78

7 years ago, David's age was 3 times Morgan's age

Making the equations:

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

Solving the equations:

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                                                             [since x = 78 - y]

78 + 14 = 4y

4y = 92

y = 23

Using this value in the first equation:

x + y = 78

x + 23 = 78                                                                  [since y = 23]

x = 55

The Age of David and Morgan:

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

1

step-by-step explanation:

it's the only multiple of both and the least

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)