Question

A jar has 570 marbles of different colors.The ratio of red to blue marbles are 2:3 and red to green is 4:5.how many marbles of each type is there?

Answer 1

The number of red marbles = 152

The number of blue marbles = 228 and

the number of green marbles = 190

Explanation:

Let x be the number of red marbles, y be the number of blue marbles and z be the number of green marbles.

It is given that the total marbles = 570.

Therefore, x + y + z = 570 --- (1)

It is also given that the ratio of red to blue marbles is 2 : 3.

Therefore, x : y = 2 : 3

or 3x = 2y --- (2)

It is also given that the ratio of red to green marbles is 4 : 5.

Therefore, x : z = 4 : 5

or 5x = 4z --- (3)

From (2),
`y=(3x)/(2)`

From (3),
`z=(5x)/(4)`

Substituting the above in (1), we get,

`x+(3x)/(2) +(5x)/(4) =570`

Multiply both sides by 4.

4x + 6x + 5x = 2280

15x = 2280

Divide both sides by 15.

x = 152

Hence,

y =
`(3(152))/(2)`

y = 228

z =
`(5(152))/(4)`

z = 190

Therefore,

The number of red marbles = 152

The number of blue marbles = 228 and

the number of green marbles = 190

Check:

Total number of marbles = 152 + 228 + 190 = 570

Ratio of red to blue marbles = 152 : 228 = 2 : 3

Ratio of red t green marbles = 152 : 190 = 4 : 5