Question

a middle school band has 45 sixth and seventh graders. The ratio of sixth graders to seventh graders is 2 to 3. How many sixth graders are in the band. Need to show work!

Answer 1

2 out of every 3 children are sixth graders
in order to solve this you have to find how many are sixth graders out of 45

45/3=15

15×2=30

30 out of 45 students are sixth graders

Answer 2

`18\ sixth\ graders`

Explanation:

Let

x-----> the number of sixth graders in the band

y-----> the number of seventh graders in the band

we know that

`x+y=45` -----> equation A

`(x)/(y)=(2)/(3)` ------> isolate the variable y

`y=(3)/(2)x` -----> equation B

Substitute equation B in equation A

`x+(1.5x)=45`

`2.5x=45`

`x=45/2.5=18\ sixth\ graders`