Question

During the first quarter of the school year, the ratio Of the number Of students in chorus to the number of students in band was 1 : 8. However, the chorus classes were really small, and the band classes were large, so the principal changed students' classes for the second quarter. In the second quarter, the ratio ofthe number of students in chorus to the ratio of the number of students in band was 5 : 4. If 75 students were in chorus the second quarter, how many were in chorus and band in the first quarter? Use a tape diagram to support your answer.

Answer 1

In the first quarter, there were 7 students in chorus and 56 students in band.

Step-by-step explanation:

To solve this problem, we can create a tape diagram to represent the number of students in chorus and band in the first quarter. Let's use the variable 'x' to represent the number of students in chorus, and '8x' to represent the number of students in band.

According to the given information, the ratio of the number of students in chorus to the number of students in band in the first quarter is 1:8. This can be represented as x:8x.

In the second quarter, the ratio of the number of students in chorus to the number of students in band is 5:4. We are also given that there were 75 students in chorus in the second quarter. So, we can set up the equation 5/4 = 75/8x.

Solving this equation, we find that 8x = 60, and x = 7.5. Since we can't have a fractional number of students, we round x down to the nearest whole number, which is 7.

Therefore, in the first quarter, there were 7 students in chorus and 8 * 7 = 56 students in band.