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?

2 Answers
May 21, 2018

Answer:

Present age of Lauren, Joshua and Jared be #27,13 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(x+3)-27 # or

#z+3 =2(2 y+1+3)-27 or z=4 y+8-27-3 # or

#z= 4 y-22 ; (2)#

#4# years ago #z - 4= 3(y-4)-1 or 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 or y =13 :. x= 2*13+1=27#

#z= 4 y -22 = 4*13-22=30 # Therefore present age of

Lauren, Joshua and Jared be #27,13 and 30# years

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

Answer:

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

#ul(color(white)(xxxxxxxx)"past" rarr+4color(white)(xxxx)"present"rarr+3color(white)(xxxx)"future")#
JOSHUA:#color(white)(xxxxxx)x color(white)(xxxxxxx)(x+4)color(white)(xxxxxxxxx)(x+7)#

LAUREN:#color(white)(xxxxccxxxx)color(white)(xxxxx)2(x+4)+1color(white)(xxxxxx)color(blue)((2x+12))#

JARED:#color(white)(xxxxx)3x-1color(white)(xxxxx)(3x-1+4)color(white)(xxxxx)color(blue)((3x+3+3))#

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.

#color(blue)(2(2x+12)-27 = 3x+6)#

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

#4x-3x =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.

#ul(color(white)(xxxxxxxx)"past" rarr+4color(white)(xxxx)"present"rarr+3color(white)(xxxx)"future")#
JOSHUA:#color(white)(xxxxxx)9 color(white)(xxxxxxxx)13color(white)(xxxxxxxxxxxx)16#

LAUREN:#color(white)(xxxxccxxxx)color(white)(xxxxxxx)27color(white)(xxxxxxxxxxxx)color(blue)(30)#

JARED:#color(white)(xxxxxxx)26color(white)(xxxxxx.x)40color(white)(xxxxxxxxxxxx)color(blue)(33)#

Check: #2xx30-27 =33#