Currently
Let Amy's current age be x. Since Dianne is 23 years older than her daughter, then she is (x + 23) years old.
In 5 years
Amy's age will be (x + 5) years.
Dianne's age will be:
[tex]x+23+5=(x+28)\text{ years}[/tex]The sum of their ages in 5 years is 91. Therefore, we have:
[tex](x+5)+(x+28)=91[/tex]Solving, we have:
[tex]\begin{gathered} x+5+x+28=91 \\ 2x=91-5-28 \\ 2x=58 \\ x=\frac{58}{2} \\ x=29 \end{gathered}[/tex]Amy is 29 years old. Therefore, Dianne will be:
[tex]29+23=52\text{ years old}[/tex]ANSWER:
Amy is 29 years old, and Dianne is 52 years old.
