six people went into the woods to look for truffles. on average they collected 7 truffles per person. the average of the first four people to come back was 8 truffles per person. in fact, the fourth person to come back had 11 truffles in his basket. how many truffles did the last three people collect altogether?

Six people went into the woods to look for truffles. On average they collected 7 truffles per person. The average of the first four people to come back was 8 truffles per person. In fact, the fourth person to come back had 11 truffles in his basket. How many truffles did the last three people collect altogether:
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calculista calculista · Answer 2 · 2018-08-11T12:13:32-04:00

Let

x1-------> number of truffles of the first person

x2-------> number of truffles of the second person

x3-------> number of truffles of the third person

x4-------> number of truffles of the fourth person

x5-------> number of truffles of the fifth person

x6-------> number of truffles of the sixth person

we know that

\(\frac{(x1+x2+x3+x4+x5+x6)}{6} =7\) ------> equation \(1\)

\(\frac{(x1+x2+x3+x4)}{4} =8\\ (x1+x2+x3+x4)=8*4\)

\((x1+x2+x3+x4)=32\) -------> equation \(2\)

\(x4=11\) -------> equation \(3\)

Substitute equation \(3\) in equation \(2\)

\((x1+x2+x3+11)=32\\ (x1+x2+x3)=32-11\)

\((x1+x2+x3)=21\) ------> equation \(4\)

Substitute equation \(4\) in equation \(1\)

\(\frac{((21)+x4+x5+x6)}{6} =7\\ \\ ((21)+x4+x5+x6)=42\\ \\ x4+x5+x6=42-21\\ \\ x4+x5+x6=21\)

therefore

the answer is

\(21\ truffles\)