Question

the ratio of seventh graders to eighth graders in the jackson middle school band is 7 to 6. there are 14 seventh graders in the band. next week, 1 more eighth grader will be joining. what will the ratio be then? seventh graders to eighth graders

Explanation:

Step1: Find number of eighth graders initially

Let the number of seventh graders be \(7x\) and eighth graders be \(6x\). Given \(7x = 14\), solve for \(x\): \(x=\frac{14}{7}=2\). So initial eighth graders: \(6x = 6\times2 = 12\).

Step2: Find new number of eighth graders

After 1 more joins, new eighth graders: \(12 + 1 = 13\).

Step3: Determine new ratio

Seventh graders remain 14, so ratio is \(14:13\).

Answer:

14 seventh graders to 13 eighth graders