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test of genius?

#3- a square cake measures 6 units by 6 units by 4 units. The cake falls into a vat of frosting and comes out frosted on all six faces. The cake is then cut up into cubes, each measuring 1 unit on each edge. how many of these cubes will have exactly one face frosted.

#8- An algebra teacher drove past a farmyard that was full of chickens and pigs. The teacher happened to notice that there were a total of 70 heads and 200 legs. How many chickens and how many pigs were there?

Volume of cake = 6 x 6 x 4
Volume of cake = 144 cube unit

Volume of each frosted face = 144/6
Volume of each frosted face = 24 cube unit

Nos. of cubes have a face = 24/1
Nos. of cubes have a face = 24

Ley pigs = a
chickens = b
according to question,
a + b = 70________________(1)
4a + 2b = 200_____________(2)

By sol. (1) & (2)
a = 30
b = 40
Pigs = 30
chickens = 40

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