Question

toward the middle of the harvesting season, peaches for canning come in three types, early, late, and extra late, depending on the expected date of ripening. during a certain week, the data to the right were recorded at a fruit delivery station. complete parts (a) through (d) below. 29 trucks went out carrying early peaches; 66 carried late peaches; 51 carried extra late peaches; 22 carried early and late; 30 carried late and extra late; 4 carried early and extra late; 2 carried all three; 8 carried only figs (no peaches at all). (a) how many trucks carried only late variety peaches? 16 trucks (type a whole number.) (b) how many carried only extra late? 19 trucks (type a whole number.) (c) how many carried only one type of peach? trucks (type a whole number.)

Explanation:

Step1: Find number of trucks with only early peaches

Number of trucks with early peaches ($n(E)$) = 29, with early and late ($n(E\cap L)$)=22, with early and extra - late ($n(E\cap EL)$)=4, with all three ($n(E\cap L\cap EL)$)=2.
Number of trucks with only early peaches = $n(E)-(n(E\cap L)+n(E\cap EL)) + n(E\cap L\cap EL)=29-(22 + 4)+2=5$.

Step2: Use results from (a) and (b)

We know from (a) that number of trucks with only late peaches = 16, from (b) number of trucks with only extra - late peaches = 19.

Step3: Calculate number of trucks with only one type of peach

Number of trucks with only one type of peach= Number of trucks with only early+Number of trucks with only late+Number of trucks with only extra - late.
$5 + 16+19 = 40$.

Answer:

40