Question

I need help with question 4.Will is w years old.Ben is 3 years older.1. Write an expression, in terms of w, for Ben's age.Jan is twice as old as Ben.2. Write an expression, in terms of w, for Jan's age.If you add together the ages of Will, Ben and Jan the total comes to 41 years.3. Form an equation and solve it to work out how old Will, Ben, and Jan are.4) in how many years time will Jan be twice as old as will?

Answer 1

We are given the following information:

Will is w years old

Ben is 3 years older

1. This is expressed as:

`\begin{gathered} Ben=w+3 \\ \Rightarrow b=w+3 \\ \\ b=w+3------------1 \end{gathered}`

2. Jan is twice as old as Ben. This is given as:

`\begin{gathered} Jan=2* b \\ \Rightarrow j=2b \\ but\colon b=w+3 \\ \Rightarrow j=2(w+3) \\ j=2w+6 \\ \\ j=2w+6-------------2 \end{gathered}`

3. If you add together the ages of Will, Ben, and Jan the total comes to 41 years. This is given as:

`w+b+j=41---------3`

4. In how many years time will Jan be twice as old as will? This is solved as shown below:

`\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=(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}`

We will proceed to solve:

Therefore, Jan will be twice as old as Will in 6 years time