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makkiz [27]
3 years ago
12

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 e

ach type is there?
Mathematics
1 answer:
iVinArrow [24]3 years ago
8 0

Answer:

The number of red marbles = 152

The number of blue marbles = 228 and

the number of green marbles = 190

Step-by-step 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=\frac{3x}{2}

From (3), z=\frac{5x}{4}

Substituting the above in (1), we get,

x+\frac{3x}{2} +\frac{5x}{4} =570

Multiply both sides by 4.

4x + 6x + 5x = 2280

15x = 2280

Divide both sides by 15.

x = 152

Hence,

y = \frac{3(152)}{2}

y = 228

z = \frac{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

<u>Check:</u>

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


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