# Lauren is 1 year more than twice Joshua’s age. 3 years from now, Jared will be 27 less than twice Lauren’s age. 4 years ago, Jared was 1 year less than 3 times Joshua’s age. How old will Jared be 3 years from now?

May 21, 2018

Present age of Lauren, Joshua and Jared be $27 , 13 \mathmr{and} 30$
years. After $3$ years Jared will be $33$ years.

#### Explanation:

Let the present age of Lauren, Joshua and Jared be

$x , y , z$ years By given condition ,  x =2 y+1; (1)

After $3$ years $z + 3 = 2 \left(x + 3\right) - 27$ or

$z + 3 = 2 \left(2 y + 1 + 3\right) - 27 \mathmr{and} z = 4 y + 8 - 27 - 3$ or

z= 4 y-22 ; (2)

$4$ years ago $z - 4 = 3 \left(y - 4\right) - 1 \mathmr{and} z - 4 = 3 y - 12 - 1$ or

 z =3 y -13+4 or z = 3 y -9 ;(3)  From equations (2) and (3)

we get $4 y - 22 = 3 y - 9 \mathmr{and} y = 13 \therefore x = 2 \cdot 13 + 1 = 27$

$z = 4 y - 22 = 4 \cdot 13 - 22 = 30$ Therefore present age of

Lauren, Joshua and Jared be $27 , 13 \mathmr{and} 30$ years

After $3$ years Jared will be $33$ years. [Ans]

May 21, 2018

Jared will be $33$ in $3$ years time.

#### Explanation:

For age problems such as these, it is useful to draw a table showing past, present and future, with a row for each person mentioned.

Choose the variable to be the youngest person's age and write an expression for all the others in terms of that variable.

Let Joshua's age $4$ years ago be $x$ years

$\underline{\textcolor{w h i t e}{\times \times \times \times} \text{past" rarr+4color(white)(xxxx)"present"rarr+3color(white)(xxxx)"future}}$
JOSHUA:$\textcolor{w h i t e}{\times \times \times} x \textcolor{w h i t e}{\times \times \times x} \left(x + 4\right) \textcolor{w h i t e}{\times \times \times \times x} \left(x + 7\right)$

LAUREN:$\textcolor{w h i t e}{\times \times \mathcal{\times} \times} \textcolor{w h i t e}{\times \times x} 2 \left(x + 4\right) + 1 \textcolor{w h i t e}{\times \times \times} \textcolor{b l u e}{\left(2 x + 12\right)}$

JARED:$\textcolor{w h i t e}{\times \times x} 3 x - 1 \textcolor{w h i t e}{\times \times x} \left(3 x - 1 + 4\right) \textcolor{w h i t e}{\times \times x} \textcolor{b l u e}{\left(3 x + 3 + 3\right)}$

Use the ages shown in blue to write an equation.
In $4$ years time, Jared's age will be $27$ less than twice Lauren's age.

$\textcolor{b l u e}{2 \left(2 x + 12\right) - 27 = 3 x + 6}$

$4 x + 24 - 27 = 3 x + 6$

$4 x - 3 x = 6 + 3$

$x = 9$

This is Joshua's age $3$ years ago. From this answer you can work out all the ages and check that they agree with the information given.

$\underline{\textcolor{w h i t e}{\times \times \times \times} \text{past" rarr+4color(white)(xxxx)"present"rarr+3color(white)(xxxx)"future}}$
JOSHUA:$\textcolor{w h i t e}{\times \times \times} 9 \textcolor{w h i t e}{\times \times \times \times} 13 \textcolor{w h i t e}{\times \times \times \times \times \times} 16$

LAUREN:$\textcolor{w h i t e}{\times \times \mathcal{\times} \times} \textcolor{w h i t e}{\times \times \times x} 27 \textcolor{w h i t e}{\times \times \times \times \times \times} \textcolor{b l u e}{30}$

JARED:$\textcolor{w h i t e}{\times \times \times x} 26 \textcolor{w h i t e}{\times \times \times . x} 40 \textcolor{w h i t e}{\times \times \times \times \times \times} \textcolor{b l u e}{33}$

Check: $2 \times 30 - 27 = 33$