Exercise 51 Page 10

Let's determine the number of girls and boys in a school marching band one at a time.

Number of Girls

Let x be the number of girls in the band. We know that one-sixth of these girls are in the percussion section. Let's write that expression down and simplify. 1/6 * x = 1/6 x What we also know is that in the percussion section there is a total of 6 girls. We can now write our equation. 1/6x = 6 Let's solve the equation by isolating x.

1/6x=6

MoveRightFacToNumOne

1/b* a = a/b

x/6=6

MultEqn

LHS * 6=RHS* 6

x/6* 6=6*6

FracMultDenomToNumber

a/6* 6 = a

x=6 * 6

Multiply

Multiply

x= 36

We found that there are 36 girls in the marching band.

Number of Boys

Let y be the number of boys in a marching band. We know that two-sevenths of these boys are in the percussion section. 2/7 y We are told that the percussion section consists of 10 boys. This gives us the following equation. 2/7 y = 10 We can now isolate y in order to solve the equation.

2/7y=10

MoveRightFacToNum

a/c* b = a* b/c

2y/7=10

MultEqn

LHS * 7=RHS* 7

2y/7 * 7=10*7

FracMultDenomToNumber

a/7* 7 = a

2y=10* 7

Multiply

Multiply

2y=70

DivEqn

.LHS /2.=.RHS /2.

y= 35

There are 35 boys in the marching band.

Total Number of Students

We calculated that there are 36 girls and 35 boys in the marching band. Let's now add these two numbers to find the total number of people in the band. 36 + 35=71 We found that there are 71 students in the marching band.