What's Ta
Try solving the following problem
In a group of 120 students, 68 had ridden a bus, 78 had ridden the LRT. 33
had ridden a jeep, while 40 had ridden both the bus and the LRT, 20 had ridden
the bus and the jeep, 19 had ridden the LRT and the jeep and 15 had ridden the
bus, the LRT and the jeep.
a. How many had ridden the bus only?
b. How many had ridden the LRT only?
c. How many had ridden the jeep only?
d. How many did not ride on any of the three modes of transportation?

Question

15-10-2020
Mathematics

contestada

What's Ta
Try solving the following problem
In a group of 120 students, 68 had ridden a bus, 78 had ridden the LRT. 33
had ridden a jeep, while 40 had ridden both the bus and the LRT, 20 had ridden
the bus and the jeep, 19 had ridden the LRT and the jeep and 15 had ridden the
bus, the LRT and the jeep.
a. How many had ridden the bus only?
b. How many had ridden the LRT only?
c. How many had ridden the jeep only?
d. How many did not ride on any of the three modes of transportation?

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fichoh fichoh · Answer 1 · 2020-10-20T09:35:58+02:00

fichoh fichoh

20-10-2020

Answer:

A.) bus only = 23

B.) LRT only = 34

C.) Jeep only = 9

D.) 5

Step-by-step explanation:

Let :

B = bus ; J = Jeep ; L = LRT

KINDLY CHECK ATTACHED PICTURE FOR DETAILED EXPLANATION

Answer Link

MrRoyal MrRoyal · Answer 2 · 2021-09-24T18:38:44+02:00

A set is a group of related item.

34 had ridden on LRT only
23 had ridden on bus only
9 had ridden on jeep only
5 did not ride on any

Let:

[tex]Total =120[/tex]

[tex]B = 68 \to Bus[/tex]

[tex]L = 78 \to LRT[/tex]

[tex]J =33 \to Jeep[/tex]

[tex]n(B\ n\ L) = 40[/tex]

[tex]n(B\ n\ J) = 20[/tex]

[tex]n(L\ n\ J) = 19[/tex]

[tex]All = 15[/tex]

(a) Bus only

This is calculated using:

[tex]B\ only = B - n(B\ n\ L) - n(B\ n\ J) + All[/tex]

So, we have:

[tex]B\ only = 68 - 40 - 20 + 15[/tex]

[tex]B\ only = 23[/tex]

(b) LRT only

This is calculated using:

[tex]L\ only = L - n(B\ n\ L) - n(L\ n\ J) + All[/tex]

So,

[tex]L\ only = 78 - 40 - 19 + 15[/tex]

[tex]L\ only = 34[/tex]

(c) Jeep only

This is calculated using:

[tex]J\ only = J - n(B\ n\ J) - n(L\ n\ J) + All[/tex]

So, we have:

[tex]J\ only = 33 - 20 - 19 + 15[/tex]

[tex]J\ only = 9[/tex]

(d) None

Let x represents those that took none of the means of transport.

So, we have:

[tex]Total = B\ only + J\ only + L\ only + [n(B\ n\ L) -All] +[n(B\ n\ J) -All] +[n(L\ n\ J) -All] + All + x[/tex]

This gives

[tex]120= 34 + 23 + 9 + [40 -15] +[20 -15] +[19 -15] + 15 + x[/tex]

[tex]120= 115 + x[/tex]

Collect like terms

[tex]x = 120 - 115[/tex]

[tex]x = 5[/tex]

See attachment for the Venn diagram of the set.