The Sun Brainboxer April 1

[LeicesterAdy]

Been racking my brains all week to no avail: A car dealer reduced the prices of four vehicles. The van has been reduced by as much as the other three put together and by eight times as much as the hatchback. The reduction in the sports car minus the reduction in the hatchback was half the reduction on the 4 x 4. The 4 x 4 was reduced by £250 more than the sports car. How much have the vehicles been reduced in total?

[JJ109]

H reduced by 250
S reduced by 750
4x4 reduced by 1000
V reduced by 2000

[JJ109]

V = 4by4 + H + S (Eq 1)
V = 8H (Eq 2)
As V is equaal in both of these
8H = 4by4 + H + S
7H = 4by4 + S (Call this Eq 3)
we also know that
(S - H) = 1/2(4by4)
Therefore 2(S - H) = 4by4 (Eq 4)
Substitute this into Equation 3
7H = 2(S - H) + S
7H = 2S - 2H + S
9H = 3S
3H = S

remember the 4by 4 = 2(S - H) = 2S - 2H
But S = 3H
4by4 = 6H -2H = 4H

Final given Equaation
4by 4 = 250 + S
Therefore 4h = 250 + 3H (converting 4by4 and S in terms of H)
H = 250
Then S = 3H = 750
Then 4by 4 = 4H = 1000
Van = 4by4 + S + H = 1000 + 750 + 250 = 2000
Then check all answers = correct