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

`((x1+x2+x3+x4+x5+x6))/(6) =7` ------> equation
`1`

`((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`

`(((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: