Final answer:
To find the number of blue marbles using the ratio 5 to 1 with 10 red marbles, divide the number of red marbles by the first number in the ratio and multiply the result by the second number in the ratio, resulting in 2 blue marbles.
Step-by-step explanation:
The student asked to find the number of blue marbles in a bag given that there are 10 red marbles and the ratio of red marbles to blue marbles is 5 to 1.
To solve this, we can use the ratio 5 to 1 means for every 5 red marbles there is 1 blue marble. Since there are 10 red marbles, which is twice the amount of 5 in the ratio, we would expect twice the number of blue marbles compared to the '1' in the ratio.
5 (red) : 1 (blue)
If we have 10 red marbles, we divide 10 by the first number in the ratio (5) to find out how many times the ratio fits into the quantity of red marbles.
10 (red marbles) / 5 (ratio red) = 2
Now multiply the second number in the ratio (1) by 2:
1 (ratio blue) × 2 = 2 blue marbles
Thus, the number of blue marbles in the bag is 2.