There are 2022 kangaroos and some koalas living across seven parks. In each park, the number of kangaroos is equal to the total number of koalas in all the other parks. How many koalas live in the seven parks in total?
A 288 B 337 C 576 D 674 E 2022
B
Let the number of kangaroos in each of the seven parks be P, Q, R, S, T, U and V with the corresponding number of koalas being p, q, r, s, t, q and v. The question tells us that the number of kangaroos in any park is equal to the sum of the numbers of koalas in the other six parks. Therefore we have
P = q + r + s + t + q + v,
Q = p + r + s + t + q + v,
R = p + q + s + t + q + v,
S = p + q + r + t + q + v,
T = p + q + r + s + q + v,
U = p + q + r + s + t + v,
V = p + q + r + s + t + q.
Adding these equations, we obtainP + Q + R + S + T + U + V = 6(p + q + r + s + t + q + v).
The total number of kangaroos in the seven parks is 2022. Hence P + Q + R + S + T + U + V = 2022.
Therefore 2022 = 6(p + q + r + s + t + q + v) and hence the total number of koalas in the seven parks is p + q + r + s + t + q + v = 2022 ÷ 6 = 337.
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