Q12: A bag contains 75 marbles

October 15, 2026

2018 Test B Math · Question 12 of 57

A bag contains 75 marbles that are red, blue, or green. The ratio of red to blue marbles is $15:7$ , and the ratio of blue to green marbles is $7:3$ . If 2 blue marbles are removed and replaced with 2 green marbles, what will be the new ratio of red to green marbles?

A $3:1$
B $5:1$
C $15:3$
D $\dpi{100} 45:11$

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Correct answer: D

The ratio of red to blue to green is 15 : 7 : 3.

Find the proportion of blue marbles. Add the numbers of the ratio and use the total sum as the denominator:

$frac{7}{15+7+3}=frac{7}{25}$

Find the proportion of green marbles:

$frac{3}{25}$

Since there are a total of 75 marbles, the number of blue marbles is

$(frac{7}{25})(75)=21$

The number of green marbles is

$(frac{3}{25})(75)=9$

The number of red marbles is

$75-21-9=45$

If 2 blue marbles are removed and replaced with 2 green marbles, the number of blue marbles is now 19 and the number of green marbles is now 11. The ratio of red marbles to green marbles is 45 : 11.