Setting up and solving quadratic equations

Original post by krisshP

Below is a question I tried, but failed.

A man is four time as old as his son, and 8 years ago the product of their ages was 160. Find their present ages as integers.

Here is my working out:

m=4s

(m-8)(s-8)=160

m-8=160

m=168

s-8=160

s=168

which means the son in 168 years old and the man is also 168. This is incorrect logically and by the answer given by my revision book. I do not understand this at all and just don't know how to tackle this question. :confused:

m-8 would not be equal to 160. That is totally irellavent to the problem.

You have deduced that m=4s, and that (m-8)(s-8)=160.
Replace m with 4s to create a quadratic function of s. try and solve from here.

(edited 11 years ago)

Reply 2

OP

Original post by CharlieBoardman

m-8 would not be equal to 160. That is totally irellavent to the problem.

You have deduced that m=4s, and that (m-8)(s-8)=160.
Replace m with 4s to create a quadratic function of s. try and solve from here.

I end up with
s=8 and s=2

But how do I know which s value I am supposed to use?

Reply 3

Original post by krisshP

I end up with
s=8 and s=2

But how do I know which s value I am supposed to use?

Your working out has gone incorrect at some point. Check it again for any mistakes in your arithmetic. Or you can post your working on here, and I can help point out your mistakes :smile:

Reply 4

OP

Original post by CharlieBoardman

Your working out has gone incorrect at some point. Check it again for any mistakes in your arithmetic. Or you can post your working on here, and I can help point out your mistakes :smile:

I forgot to minus 160 from both sides :angry:

.

s=2 and s=-12

I'll use s=2 as s=-12 is not logical.

Thanks a lot for you help. :smile:

Reply 5

Original post by krisshP

I forgot to minus 160 from both sides :angry:

.

s=2 and s=-12

I'll use s=2 as s=-12 is not logical.

Thanks a lot for you help. :smile:

I'm glad you spotted your own mistake. Unfortunately, you have made another right at the end!
You should have factorised the quadratic into (s-12)(s+2). Meaning s = -2 or 12, not the other way round!

Reply 6

Dualcore

Original post by krisshP

Below is a question I tried, but failed.

A man is four time as old as his son, and 8 years ago the product of their ages was 160. Find their present ages as integers.

Here is my working out:

m=4s

(m-8)(s-8)=160

m-8=160

m=168

s-8=160

s=168

which means the son in 168 years old and the man is also 168. This is incorrect logically and by the answer given by my revision book. I do not understand this at all and just don't know how to tackle this question. :confused:

Let m=man and s=son m=4s, (s-8)(m-8)=160 => (4s-8)(s-8)=160 =>4s^2-40s+64=160. You can go on from there.

Reply 7

OP

Original post by CharlieBoardman

I'm glad you spotted your own mistake. Unfortunately, you have made another right at the end!
You should have factorised the quadratic into (s-12)(s+2). Meaning s = -2 or 12, not the other way round!

But you'd be creating a new quadratic - I can't see the need to do so. :confused:

Why create a new quadratic? How will that lead to finding the ages? How am I supposed to know in an exam if I'm should create another quadratic.

(edited 11 years ago)

Reply 8

Original post by krisshP

But you'd be creating a new quadratic - I can't see the need to do so. :confused:

Why create a new quadratic? How will that lead to finding the ages?

No.. Here is my working out.

We know that:

m=4s

(m-8)(s-8)=160

We can sub m=4s into this to get:

(4s-8)(s-8)=160

Expand to get:

4s^2-40s-96=0

Divide by 4:

s^2-10s-24

Factorise to get:

(s-12)(s+2)

So

s=-2 or 12

(edited 11 years ago)

Reply 9

OP

CharlieBoardman -8 times -8=64

Reply 10

OP

When getting

4s^2-40s-96=0

I used the quadratic formula to get:
s=2 and s=-12

These s values are DIFFERENT ???

(edited 11 years ago)

Reply 11

OP

I'll do the quadratic formula step again.

Reply 12

Above.The.Empyrean

Greetings. :smile:

M = 4S, you've fabricated that principle.

(4S-8)(S-8)=160.

By expanding the parentheses, we obtain:

4s^2 - 40s + 64 = 160

Now, amalgamate the similar terms, (accrue similar terms onto LHS to concoct a quadratic expression).

4s^2 - 40s - 96 = 0

(divide by four to simplify)...

s^2 - 10s - 24 = 0

(s-12)(s+2) = 0.

Thus, S = 12.

(edited 11 years ago)

Reply 13

OP