Respuesta :
Nancy: n
Olivia: o
Casandra: c
Nancy is four times as old as Olivia:
[tex]n=4o[/tex]Olivia is three years less than Cassandra
[tex]o=c-3[/tex]The sum of their ages is 45:
[tex]n+o+c=45[/tex]Use the next system of equations to solve How old is each girl?:
[tex]\begin{gathered} n=4o \\ o=c-3 \\ n+o+c=45 \end{gathered}[/tex]Write all the equation in terms of c:
Substitute the o in the first equation by the value of o in the second equation:
[tex]\begin{gathered} n=4(c-3) \\ n=4c-12 \end{gathered}[/tex]Substitite in the third equation the n and o by the corresponding values in terms of c:
[tex](4c-12)+(c-3)+c=45[/tex]Solve c:
[tex]\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;} \\ \frac{6}{6}c=\frac{60}{6} \\ \\ c=10 \end{gathered}[/tex]Use the value of c to solve the other two variables;
[tex]\begin{gathered} n=4c-12 \\ n=4(10)-12 \\ n=40-12 \\ n=28 \\ \\ o=c-3 \\ o=10-3 \\ o=7 \end{gathered}[/tex]Then, Nancy is 28 years old, Olivia is 7 years old and Cassandra is 10 years old