Why is different approach giving same? "A father is 30 years old and his son is 14 years old..."

C

chijioke

Full Member
Joined
Jul 27, 2022
Messages
352
A father is 30 years old and his son is 14 years; when in the past was the product of their ages 80?
In the first approach, I said let x be the years past when the product of their ages was 80?
[math](30-x)(14-x)=80[/math] with this at the end of the solving x=10 or x=34. By main looking. The right thing is x=10 because by checking [math](30-10)(14-10)=80 \\ (20)(4)=80[/math] This means that father and son were 20 and 4 years respectively in the past.
It can't be
[math](30-34)(14-34)=80 \\ (-4)(-20)=80[/math] because ages are not negative.
If I decide to handle it this way
[math](x-30)(x-14)=80[/math] I still get x=10 or x=34. My question is why is the result the same?
 
chijioke said:
A father is 30 years old and his son is 14 years; when in the past was the product of their ages 80?
In the first approach, I said let x be the years past when the product of their ages was 80?
[math](30-x)(14-x)=80[/math] with this at the end of the solving x=10 or x=34. By main looking. The right thing is x=10 because by checking [math](30-10)(14-10)=80 \\ (20)(4)=80[/math] This means that father and son were 20 and 4 years respectively in the past.
It can't be
[math](30-34)(14-34)=80 \\ (-4)(-20)=80[/math] because ages are not negative.
If I decide to handle it this way
[math](x-30)(x-14)=80[/math] I still get x=10 or x=34. My question is why is the result the same?
Click to expand...
Because [imath](30-x)(14-x)=80 \implies x^2 - 44 x + 340 = 0[/imath] is a quadratic.
 
Alternatively you can factor -1 from each factor.

(30-x)(14-x)= -1(x-30)*-1(x-14) = -1*-1(x-30)(x-14) = 1(x-30)(x-14) = (x-30)(x-14)
 
You must log in or register to reply here.
Top