In a box, the ratio of red marbles to blue marbles is 7 : 4. Which of the following could be the total number of marbles in the box?
18
19
21
22
The ratio 7 : 4 means:
Red marbles = \(7k\)
Blue marbles = \(4k\)
(Here, \(k\) is any whole number like 1, 2, 3, …)
Total marbles = red + blue
\(\text{Total} = 7k + 4k\)
\(\text{Total} = 11k\)
So, the total must be a multiple of 11.
Check each option:
\(18\): Try dividing by 11 → \(18 \div 11\) is not a whole number.
So, 18 is not possible.
\(19\): Try dividing by 11 → \(19 \div 11\) is not a whole number.
So, 19 is not possible.
\(21\): Try dividing by 11 → \(21 \div 11\) is not a whole number.
So, 21 is not possible.
\(22\): Try dividing by 11 → \(22 \div 11 = 2\) (a whole number).
So, 22 is possible (here, \(k = 2\)).
Answer: D) 22
Because \(22 = 11 \times 2\), it fits the form \(11k\).