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}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3x%7D%7B2%7D)
From (3), ![z=\frac{5x}{4}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B5x%7D%7B4%7D)
Substituting the above in (1), we get,
![x+\frac{3x}{2} +\frac{5x}{4} =570](https://tex.z-dn.net/?f=x%2B%5Cfrac%7B3x%7D%7B2%7D%20%2B%5Cfrac%7B5x%7D%7B4%7D%20%3D570)
Multiply both sides by 4.
4x + 6x + 5x = 2280
15x = 2280
Divide both sides by 15.
x = 152
Hence,
y = ![\frac{3(152)}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%28152%29%7D%7B2%7D)
y = 228
z = ![\frac{5(152)}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%28152%29%7D%7B4%7D)
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