Question

Five times Jeff's age plus three times Karen's age equals 92. Karen's age is 4 more than Jeff's age. How old is Karen?

Answer 1

We have to express each statement as an equation.

Five times Jeff's age plus three times Karen's age equals 92.

`5J+3K=92`

Where J is Jeff's age, and K is Karen's age.

Karen's age is 4 more than Jeff's age.

`K=J+4`

Now, we replace the second equation with the first one.

`\begin{gathered} 5J+3(J+4)=92 \\ 5J+3J+12=92 \\ 8J=92-12 \\ 8J=80 \\ J=(80)/(8) \\ J=10 \end{gathered}`

Jeff is 10 years old.

Then, we find Karen's age.

`\begin{gathered} K=J+4 \\ K=10+4 \\ K=14 \end{gathered}`

Therefore, Karen's age is 14.