Question

The number of red, blue, and green marbles in a bag is in the ratio 3: 4: 6. If 20 red marbles, 15 blue marbles, and an unknown number of green marbles are added to the bag, the ratio of red, blue, and green marbles becomes 4: 5: 7. Determine the number of green marbles added.

• A. 3
• B. 5
• C. 7
• D. 9

Answer 1

Answer:

B. 5

Let the original numbers be in ratio (3:4:6):

So,

• Red = (3x)

• Blue = (4x)

• Green = (6x)

After adding:

• Red = (3x + 20)

• Blue = (4x + 15)

• Green = (6x + g) (where (g) is added green marbles)

New ratio is (4:5:7), so:

$\frac{3x+20}{4} = \frac{4x+15}{5} = \frac{6x+g}{7}$

Step 1: Use first two ratios

$\frac{3x+20}{4} = \frac{4x+15}{5}$

Cross multiply:

$5(3x+20) = 4(4x+15)$
$15x + 100 = 16x + 60$
100 - 60 = 16x - 15x
40 = x

Step 2: Find green marbles added

Original green:
$6x = 6 \times 40 = 240$
New green:

$\frac{6x + g}{7} = \frac{240 + g}{7}$

Use equality with red:
$\frac{3x+20}{4} = \frac{120+20}{4} = \frac{140}{4} = 35$

So:
$\frac{240 + g}{7} = 35$
$240 + g = 245$
g = 5

Final Answer:

=5