Eleanor’s Elephant Emporium has four types of elephant. There are twice as many grey elephants as pygmy elephants, three times as many white elephants as grey elephants and four times as many pink elephants as white elephants. There are 20 more white elephants than pygmy elephants. How many elephants are in Eleanor’s Emporium?
A. 123
B. 132
C. 213
D. 231
E. 312
B. 132
Let the numbers of grey, pygmy, pink and white elephants be g, y, p and w respectively.
Then g = 2y . . . [1], w = 3g . . . [2], p = 4w . . . [3] and w = y + 20 . . . [4].
From [1] and [2] we get w = 3 × 2y = 6y. Substituting for w in [4] gives 6y = y + 20. So y = 4.
Therefore, w = 6 × 4 = 24, g = w ÷ 3 = 24 ÷ 3 = 8 and p = 4w = 4 × 24 = 96.
Hence the number of elephants in Eleanor’s Emporium is g + y + p + w = 8 + 4 + 96 + 24 = 132.
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