Solution:
Given the data below:
From the question, 25 years is devoted to eating and working. Also, the number of years working will exceed the number of years eating food by 19 year.
Let x represent the number of years devoted to eating food and y represent the number of years devoted to workings.
Thus,
[tex]\begin{gathered} x\Rightarrow number\text{ of years for eating food} \\ y\Rightarrow number\text{ of years for working} \end{gathered}[/tex]
Thus, we have
[tex]\begin{gathered} x+y=25\text{ ---equation 1} \\ y=x+19\text{ ---- equation 2} \end{gathered}[/tex]
To solve the above simultaneous equations by substitution, we substitute equation 2 into equation 1.
Thus,
[tex]\begin{gathered} x+(x+19)=25 \\ open\text{ parentheses,} \\ x+x+19=25 \\ \Rightarrow2x+19=25 \\ subtract\text{ 19 from both sides of the equation,} \\ 2x+19-19=25-19 \\ \Rightarrow2x=6 \\ divide\text{ both sides by the coefficient of x, which is 2} \\ \frac{2x}{2}=\frac{6}{2} \\ \Rightarrow x=3 \end{gathered}[/tex]
Substitute the value of 3 for x into equation 2.
Thus,
[tex]\begin{gathered} y=x+19 \\ where\text{ x=3} \\ y=3+19 \\ \Rightarrow y=22 \end{gathered}[/tex]
Hence,
22 years will be spent on working and 3 years will be spent on eating food.
