Question

An urn contains marbles of four colors: red, yellow, blue, and green. All but 45 of the marbles are red; all but 45 are yellow; all but 45 are blue; and all but 60 are green. How many of the marbles are green?

Answer 1

Answer:

5

Step-by-step explanation:

Let the number of

red marbles be r

blue marbles be b

yellow marbles be y and

green marbles be g

Let the Total number of marbles be T then

r + y + b + g = T

If all but 45 of the marbles are red then

y + b + g = 45

As such, r + 45 = T

all but 45 are yellow;

r + b + g = 45

As such, y + 45 = T

all but 45 are blue;

y + r + g = 45

As such, b + 45 = T

It means that the number of red, yellow and blue marbles are equal

Hence y = b = r

If all but 60 are green

y + b + r = 60

y + y + y = 60

3y = 60

y = 60/3 =20

This means that there are 20 yellow marbles, 20 red marbles and 20 green marbles

The total number of marbles T = 20 + 45 = 65

As such, g + 60 = T

g + 60 = 65

g = 65 - 60

= 5 marbles

Answer 2

There are 5 marbles which are in green color.

Let us consider that red, yellow, blue, and green marbles are represented by r, y, b  and g respectively.

Total number of marbles are represented by T .

All but 45 of the marbles are red;

                                   $T-45=r ........(1)$

All but 45 are yellow,

                                    $T-45=y...........(2)$

All but 45 are blue,

                                 $T-45=b..............(3)$

From equation 1 , 2 and 3

We observe that,

                                $r=y=b$

Since, all but 60 are green,  $T-60=g$

                $T=r+y+b+g\\\\r+y+b+g-60=g\\\\r+y+b=60\\\\3y=60\\\\y=20\\\\r=y=b=20$

Now, Total number of marbles $=45+20=65$

Number of green marbles$=65-60=5$

Therefore, There are 5 marbles which are in green color.

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