Question

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?

Answer 1

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

$21\ truffles$

Answer 2

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:
please see the attachment for mathematical work: