QuestionTrucks carried peaches: 34 early, 61 late, 50 extra late. Find trucks with only late, only extra late, only one type, and total.

Studdy Solution

STEP 1

Assumptions1. The number of trucks carrying early peaches is34. . The number of trucks carrying late peaches is61.
3. The number of trucks carrying extra late peaches is50.
4. The number of trucks carrying both early and late peaches is25.
5. The number of trucks carrying both late and extra late peaches is30.
6. The number of trucks carrying both early and extra late peaches is8.
7. The number of trucks carrying all three types of peaches is6.
8. The number of trucks carrying only figs is9.

STEP 2

First, we need to find the number of trucks carrying only late variety peaches. We can do this by subtracting the number of trucks carrying both early and late peaches, both late and extra late peaches, and all three types of peaches from the total number of trucks carrying late peaches.
$Only\, late\, peaches = Total\, late\, peaches - (Early\, and\, late\, peaches + Late\, and\, extra\, late\, peaches + All\, three\, types)$

STEP 3

Now, plug in the given values to calculate the number of trucks carrying only late peaches.
$Only\, late\, peaches =61 - (25 +30 +6)$

STEP 4

Calculate the number of trucks carrying only late peaches.
$Only\, late\, peaches =61 - (25 +30 +6) =0$

STEP 5

Next, we need to find the number of trucks carrying only extra late peaches. We can do this by subtracting the number of trucks carrying both late and extra late peaches, both early and extra late peaches, and all three types of peaches from the total number of trucks carrying extra late peaches.
$Only\, extra\, late\, peaches = Total\, extra\, late\, peaches - (Late\, and\, extra\, late\, peaches + Early\, and\, extra\, late\, peaches + All\, three\, types)$

STEP 6

Now, plug in the given values to calculate the number of trucks carrying only extra late peaches.
$Only\, extra\, late\, peaches =50 - (30 +8 +6)$

STEP 7

Calculate the number of trucks carrying only extra late peaches.
$Only\, extra\, late\, peaches =50 - (30 + +6) =6$

STEP 8

To find the number of trucks carrying only one type of peach, we need to add the number of trucks carrying only early peaches, only late peaches, and only extra late peaches.
$Only\, one\, type = Only\, early\, peaches + Only\, late\, peaches + Only\, extra\, late\, peaches$

STEP 9

Now, plug in the given values to calculate the number of trucks carrying only one type of peach.
$Only\, one\, type =34 - (25 +8 +6) + +6$

STEP 10

Calculate the number of trucks carrying only one type of peach.
$Only\, one\, type =34 - (25 +8 +6) +0 +6 =$

STEP 11

Finally, to find the total number of trucks that went out during the week, we need to add the number of trucks carrying each type of peach and the number of trucks carrying only figs.
$Total\, trucks = Early\, peaches + Late\, peaches + Extra\, late\, peaches + Only\, figs$

STEP 12

Now, plug in the given values to calculate the total number of trucks that went out during the week.
$Total\, trucks =34 +61 +50 +9$

STEP 13

Calculate the total number of trucks that went out during the week.
$Total\, trucks =34 +61 +50 +9 =154$ (a) The number of trucks carrying only late variety peaches is0. (b) The number of trucks carrying only extra late peaches is6. (c) The number of trucks carrying only one type of peach is. (d) The total number of trucks that went out during the week is154.

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