# Question #def8e

Nov 22, 2017

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:
$81 = 2 p + 15$
$2 p = 66$
$p = 33$

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.

Nov 22, 2017

Pat is 33 and Dakota is 48

#### Explanation:

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

Pat's age now . . . . . . . $x$ $\leftarrow$ the number of years in Pat's age
15 years older . . . . . . . $x + 15$ $\leftarrow$ Dakota's age

In nine years, their ages will be:
Pat . . . . . . $x + 9$ $\leftarrow$ Pat's future age
Dakota . . .$x + 15 + 9$ $\leftarrow$ 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 ]

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

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

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

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

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!