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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.
36 trucks went out carrying early peaches:
62 carried late peaches;
57 carried extra late peaches,
23 carried early and late,
30 carried late and extra late,
13 carried early and extra late,
4 carried all three:
7 carried only figs (no peaches at all).
(a) How many trucks carried only late variety peaches?
trucks
(Type a whole number.)
(b) How many carried only extra late?
trucks
(Type a whole number.)
(c) How many carried only one type of peach?
trucks
(Type a whole number.)
(d) How many trucks (in all) went out during the week?
trucks
(Type a whole number.)

Answer 1

Based on the method of solutions of equations, the number of Trucks carrying the fruits are as follows:

• Late Peach only = 17 trucks
• Extra late Peach only = 22 trucks
• Trucks that carried only one type of peach = 47 trucks
• Total number of trucks = 108 trucks

What is the solution of an equation?

The solution of an equation makes the equation true.

How to solve for the number of Trucks

From the data provided:

36 trucks went out carrying early peaches:

62 carried late peaches;

57 carried extra late peaches,

23 carried early and late,

30 carried late and extra late,

13 carried early and extra late,

4 carried all three:

7 carried only figs (no peaches at all).

The number of trucks that carry only late variety peaches:

Late Peach only = 63 - (30 - 4) - (24 - 4)

• Late Peach only = 17 trucks

Number of Trucks that carried only extra late variety peach:

Extra late Peach only = 57 - (30 - 4) - (13 - 4)

• Extra late Peach only = 22 trucks

Number of Trucks that carried only one type of peach?

Early Peach only = 36 - (13 - 4) - (23 - 4)

Early Peach only = 8 trucks

Then;

Number of Trucks that carried only one type of peach = 17 + 22 + 8

• Trucks that carried only one type of peach = 47 trucks

Total number of trucks that went out during the week:

Total number of Trucks = 47 + (13 - 4) + (23 - 4) + (30 - 4) + 7

• Total number of trucks = 108 trucks

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