Little Johnny was pestering his big brother for some candy. He knew that his brother had several pieces and wanted some.
His brother had Quick Quackers, Tangy Toffees, Fizzy Booms, Apple Chewies, Purple Plops, Zounds!, Sour Screams and Buzzy Bites.
Little Johnny’s favourites were Tangy Toffee and Quick Quackers. His brother said he’d give him all of those that he had if he could figure out how many Tangy Toffees and Quick Quackers he had in his room.
He told Little Johnny the following clues:
- If he added all the Buzzy Bites, the Purple Plops and Fizzy Booms that he had, the total was 48.
- If he added the number of Apple Chewies and Buzzy Bites, it was the same as the number of Zounds! he had.
- If he added the number of Zounds! and the Purple Plops, it was the same as the number of Tangy Toffees he had.
- If he added the number of Tangy Toffees and the Apple Chewies, it was the same as the number of Fizzy Booms he had.
- If he added the number of Fizzy Booms and the Sour Screams, it was the same as the number of Quick Quackers he had.
- Finally, he told him that if you subtracted the number of Tangy Toffees from the Quick Quackers, he would have the number 14.
Little Johnny took a few minutes, but walked away with all the Tangy Toffees and Quick Quackers, even though his mother had to make his brother honour his promise. Can you figure out how many Quick Quackers and Tangy Toffees that Little Johnny got?
Answer
Apple Chewies = A
Buzzy Bites = B
Fizzy Booms = F
Purple Plops = P
Quick Quackers = Q
Sour Screams = S
Tangy Toffees = T
Zounds! = Z
The explanation is as follows: - B + P + F = 48
- A + B = Z
- Z + P = T
- T + A = F
- F + S = Q
- Q—T = 14
Now, moving a few things around we find the following:
B = Z—A (from given #2)
P = T—Z (from given #3)
F = T + A (from given #4)
Then B + P + F = (Z—A) + (T—Z) + (T + A) = 2T once you add and subtract it all.
Since B + P + F = 48 = 2T.
As such, T = 24.
And from given #6, Q = 14 + T = 38
So, Q = 38 and T = 24
