Lisa's and her dad's ages combined are 51. Her dad's age is 4 less than 4 times her age. How old is Lisa?

Dec 20, 2016

$L = 9.4$ years

or $9$ years $3$ months

Explanation:

Lisa's age: $L$
Dad's age: $D$
Lisa's age and Dad's age combined is 51: $L + D = 51$
Dad's age is 4 less than 4 times her (Lisa's) age: $D = 4 L - 4$

You have a value for $D$ that is $4 L - 4$, so substitute that into the other equation:
$L + \setminus \stackrel{\left(4 L - 4\right)}{\setminus \cancel{D}} = 51 \setminus \rightarrow L + \left(4 L - 4\right) = 51$
Adding like terms, $5 L - 4 = 51$
Add 4 to each side, canceling out the left: $5 L = 51 - 4 = 47$
Dividing both sides by 5, canceling out the left: $L = \frac{47}{5} = 9.4$

9.4 years, or $9 \frac{1}{4} \setminus \leftrightarrow$ $9$ years $3$ months