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The band has 30 more members than the school chorale. If each group had 10 more members, the ratio of their membership would be 3:2. How many members are in the band? a. 50 members c. 80 members b. 45 members d. 32 members

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boffeemadrid

Answer:

80 members

Step-by-step explanation:

Let the band members be= b and the chorale members=  c

Then, according to question, b=c+30 and [tex]\frac{b+10}{c+10}=\frac{3}{2}[/tex]

⇒[tex]2(b+10)=3(c+10)[/tex]

⇒[tex]2b+20=3c+30[/tex]

⇒[tex]2b-3c=30-20[/tex]

⇒[tex]2b-3c=10[/tex]

Now, substituting the value of b=c+30, we get

⇒[tex]2(c+30)-3c=10[/tex]

⇒[tex]2c+60-3c=10[/tex]

⇒[tex]-c=-50[/tex]

⇒[tex]c=50[/tex]

Therefore, [tex]b=c+30[/tex]

[tex]b=50+30=80[/tex]

Therefore, there are 80 members in the band.

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