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 unknownnumber 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 initial numbers of red, blue, and green marbles be:

$3x,\ 4x,\ 6x$

After adding marbles:

• Red (= 3x+20)

• Blue (= 4x+15)

• Green (= 6x+y)

Given new ratio:

$(3x+20):(4x+15):(6x+y)=4:5:7$

Using the first two parts:

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

Cross multiply:

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

Now use the green ratio:

$\frac{3x+20}{6x+y}=\frac{4}{7}$

Substitute (x=40):

$\frac{140}{240+y}=\frac{4}{7}$

Cross multiply:

$980=960+4y$
$4y=20$
$y=5$

Therefore, the number of green marbles added is 5.