Three boys, Pedro, Quincy and Ralph, and their sisters, Sandy, Trixie and Vera(n

Question

Three boys, Pedro, Quincy and Ralph, and their sisters, Sandy, Trixie and Vera(not necessarily in that order), had chickens for pets.
Last week was an unusual one. Each chicken laid as many eggs as its owner owned chickens. Quincy had three times as many chickens as his own sister, and had eight more chickens than Ralph's sister. Furthermore, by the end of the week, Quincy had collected 56 more eggs than Pedro; Ralph had collected 52 more than Sandy; and Pedro had collected as many eggs as Sandy and Trixie toghther.
How many chickens did each of the six people own? And, who was whose sister?

Explanation / Answer

This should help you get started... The way to solve a word problem is to formulate the equations which the word problem is describing and then solve them mathematically. So let's label the number of chickens that each person has by their first initial (three boys P, Q, and R, and the three girls S, T, V). Then we are told: Q=3S or 3T or 3V (depending on who his sister is) Q=8+(S or T or V) (depending on who Ralph's sister is) Q=P+56 R=S+52 P=S+T Notice that Q=P+56=S+T+56 (by substituting P=S+T). If Q=8+S (or 8+T) then we end up with 8+S=S+T+56 (or 8+T=S+T+56) and by subtracting we get 8=T+56 (or 8=S+56) which results in T=-48 (or S=-48). But no one can have a negative number of chickens, so it must be that Q=8+V (and thus Ralph's sister is Vera). Since last week everyone's chickens doubled, we know everyone must have an even number of chickens. See if you can finish from here.

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