Question

Nancy is four times as old as Olivia.Olivia is three years less thanCassandra. The sum of their ages is 45.How old is each girl?

Answer 1

Nancy: n

Olivia: o

Casandra: c

Nancy is four times as old as Olivia:

`n=4o`

Olivia is three years less than Cassandra

`o=c-3`

The sum of their ages is 45:

`n+o+c=45`

Use the next system of equations to solve How old is each girl?:

`\begin{gathered} n=4o \\ o=c-3 \\ n+o+c=45 \end{gathered}`

Write all the equation in terms of c:

Substitute the o in the first equation by the value of o in the second equation:

`\begin{gathered} n=4(c-3) \\ n=4c-12 \end{gathered}`

Substitite in the third equation the n and o by the corresponding values in terms of c:

`(4c-12)+(c-3)+c=45`

Solve c:

`\begin{gathered} 4c-12+c-3+c=45 \\ \\ \text{Combine like terms:} \\ 6c-15=45 \\ \\ Add\text{ 15 in both sides of the equation:} \\ 6c-15+15=45+15 \\ 6c=60 \\ \\ \text{Divide both sides of the equation into 6;} \\ (6)/(6)c=(60)/(6) \\ \\ c=10 \end{gathered}`

Use the value of c to solve the other two variables;

`\begin{gathered} n=4c-12 \\ n=4(10)-12 \\ n=40-12 \\ n=28 \\ \\ o=c-3 \\ o=10-3 \\ o=7 \end{gathered}`Then, Nancy is 28 years old, Olivia is 7 years old and Cassandra is 10 years old