Question 24020
1. Mrs Kwok = 3x+6
Daughter's age =x


Eight years ago = 3x+6-8 (mrs Kwok)
Eight years ago = x-8 (daughter's age)



3x+6-8=9(x-8)-2
3x-2=9x-72-2-2
-6x-2=-74
-6x=-72 Divide both sides by -6
x = 12


3(12)+6=42


Hence Mrs. Kwok is 42 years old and her daughter is 12 years old.


2. Paul's age = x
Kent's age = y


7x+4y=111
4y=111-7x
y=27.75-1.75x (subsitution)


"Kent is 1 year less than four times as old as Paul is"
Kent = y
Paul = 4x-1


y=4x-1 (substitute)
(27.75-1.75x)=4x-1  simplify
28.75=5.75x
x=5


y=27.75-1.75(5)
y=19


Hence Paul is 19 and Kent is 5.


Check: 4(19) + 7(5) = 111
Paul.