2023 Mathematics Competition

### Questions 30

• Mathematics
• Maths
• Competition
• 2023

1 year ago

Though @imaculate got it first @Akintola showed more explanation, So Akintola gets it . Congrats

###### Akinola Ajayi
1 year ago

x+y=2|x-y|>>>i
xy=675...ii
From eqn i square both side to eliminate the absolute
(x+y)²=4(x-y)²
x²+2xy+y²=4x²-8xy+4y²
Equate all to 0
3x²-10xy+3y²=0>>>iii
Sub eqn ii into iii
3x²-10(675)+3y²=0
3(x²+y²)=6750
Divide both side by 3
x²+y²=2250
(x+y)²-2xy=2250
(x+y)²=2250-2(675)
(x+y)²=3600
Square root both side
x+y=60
x=60-y>>>>iv
sub eqn iv into ii
y(60-y)=675
60y-y²=675
y²-60y+675=0
Using factorisation method
y=15or 45
Sub y=15 or 45 into eqn iv
X=60-15 or 60-45
x=45 or 15.

Olusola's age 5years time will be x+5= 15+5 or 45 +5 =20yrs or 50yrsold

Dara's in 10years time will be y+10 = 15+10 or 45+10= 25yrs old or 55yrs old

###### Immaculate Nzekwe
1 year ago

Olusola's current age = 45
Dara's current age = 15

Olusola's age in 5yrs =45+5= 50yrs
Dara's age in 10 yrs= 15+10 = 25 yrs