# Extremely Hard GCSE Maths Question

Can anyone help me with this extremely hard GCSE Maths question.

Its a Non-Calculator question.

Thanks
Easy, form simultaneous equations

3+c= 2
3+a= 3

3+c-2=1
3+a+2= 2
Original post by ghen_chude_che
Easy, form simultaneous equations

3+c= 2
3+a= 3

3+c-2=1
3+a+2= 2

Thankyou
(edited 6 years ago)
Original post by ghen_chude_che
Easy, form simultaneous equations

3+c= 2
3+a= 3

3+c-2=1
3+a+2= 2

From your first equation 3 + c = 2, you get the starting number of children as -1.
Original post by zazzyhazzy

This is wrong I'm afraid.
Original post by haarithiop
This is wrong I'm afraid.

And why so?
I think I've seen this kind of question before and I got it right by stumbling around but let me attempt it.

If in doubt, call the master @_gcx.

Anyway, after a quick check in my revision guide I've got this:

c:a

(c + 3) : (a + 3) = 2:3
(c + 1) : (a + 5) = 1:2

then turn the ratios into fractions...

c+3/a+3 = 2/3
c+1/a+5 = 1/2

cross multiply...

3c + 9 = 2a + 6
2c + 2 = a + 5

rearrange...

1) 3c - 2a = -3
2) 2c -a = 3

solve them like simultaneous equations

1) 3c - 2a = -3
2) 2c -a = 3 X2 = 3) 4c - 2a = 6

3) 4c - 2a = 6
- 1) 3c - 2a = -3

= c = 9
9 CHILDREN

Subs. into 1)

1) 3c - 2a = -3
is now
3(9) - 2a = -3
27 - 2a = -3 (minus 27)
-2a = -30 (divide by -2)
a = 15

Ratio = 9:15 but it says in lowest terms so the ratio is 3:5
(edited 6 years ago)
Original post by zazzyhazzy
And why so?

3x9 =27 not 18
Original post by StudyJosh
I think I've seen this kind of question before and I got it right by stumbling around but let me attempt it.

If in doubt, call the master @_gcx.

Anyway, after a quick check in my revision guide I've got this:

c:a

(c + 3)a + 3) = 2:3
(c + 1)a + 5) = 1:2

then turn the ratios into fractions...

c+3/a+3 = 2/3
c+1/a+5 = 1/2

cross multiply...

3c + 9 = 2a + 6
2c + 2 = a + 5

rearrange...

1) 3c - 2a = -3
2) 2c -a = 3

solve them like simultaneous equations

1) 3c - 2a = -3
2) 2c -a = 3 X2 = 3) 4c - 2a = 6

3) 4c - 2a = 6
- 1) 3c - 2a = -3

= c = 9
9 CHILDREN

Subs. into 1)

1) 3c - 2a = -3
is now
3(9) - 2a = -3
27 - 2a = -3 (minus 27)
-2a = -30 (divide by -2)
a = 15

Ratio = 9:15 but it says in lowest terms so the ratio is 3:5

Correct
Original post by haarithiop
3x9 =27 not 18

Ohhhh crap hahaha didn't see that lol...anyway thanks for correcting me!
Original post by ghen_chude_che
Easy, form simultaneous equations

3+c= 2
3+a= 3

3+c-2=1
3+a+2= 2

This is wrong
Original post by StudyJosh
I think I've seen this kind of question before and I got it right by stumbling around but let me attempt it.

If in doubt, call the master @_gcx.

Anyway, after a quick check in my revision guide I've got this:

c:a

(c + 3) : (a + 3) = 2:3
(c + 1) : (a + 5) = 1:2

then turn the ratios into fractions...

c+3/a+3 = 2/3
c+1/a+5 = 1/2

cross multiply...

3c + 9 = 2a + 6
2c + 2 = a + 5

rearrange...

1) 3c - 2a = -3
2) 2c -a = 3

solve them like simultaneous equations

1) 3c - 2a = -3
2) 2c -a = 3 X2 = 3) 4c - 2a = 6

3) 4c - 2a = 6
- 1) 3c - 2a = -3

= c = 9
9 CHILDREN

Subs. into 1)

1) 3c - 2a = -3
is now
3(9) - 2a = -3
27 - 2a = -3 (minus 27)
-2a = -30 (divide by -2)
a = 15