Answer:
[tex]Age\ of\ Henry=40\ years\\\\Age\ of\ Cheryl=17\ years[/tex]
Step-by-step explanation:
[tex]Let\ age\ of\ Cheryl=x\\\\Henry\ is\ 6\ more\ than\ two\ times\ age\ of\ Cheryl\\\\\Rightarrow Age\ of\ Henry=2\times x+6=2x+6[/tex]
After 10 years:
[tex]Age\ of\ Cheryl=x+10\\\\Age\ of\ henry=2x+6+10=2x+16\\\\Sum\ of\ age=77\\\\x+10+2x+16=77\\\\3x+26=77\\\\3x=77-26\\\\3x=51\\\\x=17\\\\Age\ of\ Cheryl=17\ years\\\\Age\ of\ Henry=2\times 17+6=34+6\\\\Age\ of\ Henry=40\ years[/tex]
