Fish, Planes, and FlagsMath brain teasers require computations to solve.
David's father is in charge of decorating the 2-layer cake for Great Grampa's birthday. Great Grampa's birthday is on the Fourth of July, he used to be a pilot, and he loves fishing. David and his father have decided to decorate the sides of the bottom layer of the cake (measuring 9 in. * 15 in.) with fish and the sides of the top layer (6 in. * 9 in.) with airplanes. They are going to wrap a flag around each corner of both layers. Each decoration is 1 inch wide, and each flag is folded so that one-half inch of flag shows at each side of the corner.
Show one corner of one layer with the Polish flag in place, with 1/2 of the flag visible on each side.
"We need 2 inches between all decorations," says David's father. "Otherwise it will look too crowded."
How many decorations of each kind do David and his father need?
HintStart with a diagram of the longest side, and plan the arrangement for that side. Don't forget the flags!
AnswerDavid and his father need 8 flags, 12 fish, and 6 airplanes.
David and his father will place 12 fish decorations along the bottom layer of the cake.
Each of the longer sides of the bottom layer measures 15 in. Allowing 1/2 in. at each end for the flags and 2 in. between all the 1 in. decorations, they can place 4 fish along each 15 in. side like this:
(flag) (fish) (fish) (fish) (fish) (flag)
1/2 in. +2 in. +1 in. +2 in. +1 in. +2 in. + 1 in. +2 in. +1 in. +2 in. + 1/2 in. = 15 in.
Each of the shorter sides of the bottom layer measures 9 in. They can place 2 fish along this short side:
(flag) (fish) (fish) (flag)
1/2 in. +2 in. +1 in. +2 in. +1 in. +2 in. + 1/2 in. = 9 in.
Altogether, they can fit 12 fish (4 + 4 + 2 + 2 = 12) along the bottom layer.
The longer side of the top layer is the same length as the shorter side of the bottom layer. David and his father can fit 4 (2 + 2) airplanes on the longer sides of the top layer.
On each 6-in. side of the top layer they can fit just 1 airplane, like this:
(flag) (plane) (flag)
1/2 in. + 2 in. + 1 in. + 2 in. + 1/2 in. = 6 in.
Altogether, they can fit 6 airplanes (2 + 2 + 1 + 1 = 6) on the top layer.
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