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), [tex]y=\frac{3x}{2}[/tex]
From (3), [tex]z=\frac{5x}{4}[/tex]
Substituting the above in (1), we get,
[tex]x+\frac{3x}{2} +\frac{5x}{4} =570[/tex]
Multiply both sides by 4.
4x + 6x + 5x = 2280
15x = 2280
Divide both sides by 15.
x = 152
Hence,
y = [tex]\frac{3(152)}{2}[/tex]
y = 228
z = [tex]\frac{5(152)}{4}[/tex]
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
