Respuesta :
We are given the following information:
Will is w years old
Ben is 3 years older
1. This is expressed as:
[tex]\begin{gathered} Ben=w+3 \\ \Rightarrow b=w+3 \\ \\ b=w+3------------1 \end{gathered}[/tex]2. Jan is twice as old as Ben. This is given as:
[tex]\begin{gathered} Jan=2\times b \\ \Rightarrow j=2b \\ but\colon b=w+3 \\ \Rightarrow j=2(w+3) \\ j=2w+6 \\ \\ j=2w+6-------------2 \end{gathered}[/tex]3. If you add together the ages of Will, Ben, and Jan the total comes to 41 years. This is given as:
[tex]w+b+j=41---------3[/tex]4. In how many years time will Jan be twice as old as will? This is solved as shown below:
[tex]\begin{gathered} b=w+3------1 \\ j=2w+6-----2 \\ w+b+j=41---3 \\ We\text{ will solve using Substitution Method. Substitute ''j'' \& 'b'' into equation 3, We have:} \\ w+(w+3)+(2w+6)=41 \\ 4w+9=41 \\ \text{Subtract ''9'' from both sides, we have:} \\ 4w=41-9 \\ 4w=32 \\ w=\frac{32}{4}=8 \\ w=8 \\ \text{Substitute ''w=8'' into the equation 1, we have:} \\ b=8+3=11 \\ b=11 \\ \text{Substitute ''w=8'' into the equation 2, we have:} \\ j=2(8)+6 \\ j=16+6 \\ j=22 \\ \\ \therefore w=8,b=11,j=22 \end{gathered}[/tex]We will proceed to solve:
[tex]\begin{gathered} j=22,w=8 \\ In\text{ ''x'' years, Jan will be twice as old Will (let the number of years be represented as ''x''). This is given by:} \\ j+x=2(w+x) \\ 22+x=2(8+x) \\ 22+x=16+2x \\ \text{Put like terms together, we have:} \\ 2x-x=22-16 \\ x=6 \\ \\ Check\colon In\text{ 6 years time,} \\ Jan=22+6=28\text{ years} \\ Will=8+6=14\text{ years} \\ 28=2\cdot14\Rightarrow28=28(TRUE) \\ \end{gathered}[/tex]Therefore, Jan will be twice as old as Will in 6 years time
