Question

Question #def8e

Answer 1

Dakota is 48 years old and Patricia is 33 years old.

Explanation:

Let `d` represent the age of Dakota, and `p` the age of Patricia.

The first statement Dakota is 15 years older than Patricia tells us that:
`d = p + 15`

Our second statement in 9 years, the sum of their ages will be 99 tells us that:
`d + 9 + p + 9 = 99`
We can simplify this equation to give:
`d + p + 18 = 99`
`d + p = 81`
`d = 81 - p`

Substituting the second simplified equation into the first original equation:
`81 - p = p + 15`
Simplifying this:
`81 = 2p + 15`
`2p = 66`
`p = 33`

Finally, substituting `p = 33` into the original equation gives:
`d = 33 + 15`
`d = 48`

Check:

• 48 is indeed 15 more than 33.
• `33 + 9 = 42`
  `48 + 9 = 57`
  `57 + 42 = 99` So yes, the second statement is also true.

Conclusion:

Dakota is 48 years old and Patricia is 33 years old.

Answer 2

Pat is 33 and Dakota is 48

Explanation:

Let `x` equal the number of years in Pat's age now.

Pat's age now . . . . . . . `x` `larr` the number of years in Pat's age
15 years older . . . . . . . `x + 15` `larr` Dakota's age

In nine years, their ages will be:
Pat . . . . . . `x + 9` `larr` Pat's future age
Dakota . . .`x + 15 + 9` `larr` Dakota's future age

The sum of those future ages is 99.
[Pat's future age} "plus" [Dakota's future age] "equals" [ 99 }
[ . . . . `x + 9` . . . .]. . `+`.. [. . . `x + 15 + 9` . . . ]. . .`=`. . . [ 99 ]

`(x + 9) + (x + 15 + 9) = 99`
Solve for `x`, already defined as "Pat's age now."

1) Combine like terms
`2x + 33 = 99`

2) Subtract 33 from both sides to isolate the `2x` term
`2x = 66`

3) Divide both sides by 2 to isolate `x`, already defined as "Pat's age now."
`x = 33` `larr` answer for "Pat's age now"
Dakota is 15 years older, which is 48.

Answer:
Pat is 33 years old now.
Dakota's present age is 48
.........................

Check
Their ages in 9 years should add up to 99

In 9 years, Pat will be 42
In 9 years, Dakota will be 57
`42 + 57 = 99`

The total of those ages does equal 99
Check!