Question

PLEASE help me answer these questions! It would be greatly appreciated!!!

1) The student council conducts a fundraising project for needy families. The school board agrees to give an additional amount equal to 70% of what is raised. The Chamber of Commerce agrees to give an additional amount equal to 60% of what is raised. Here's the catch! The Board will pay 70% of the total from the project and from the Chamber of Commerce. The Chamber will pay 60% of the total from the project and from the school board. The project makes $2000. How much will the School Board give, and how much will the Chamber of Commerce give?


2) The marching band and the pep squad do a combined routine in which they divide into 5-member and 3-member groups, as shown below. If the hand has a total of 100 members and the pep squad has a total of 80 members, how many of each kind of group can be formed so that no one is left over?


Groups for equation # 2


B P B P B

P P B

Answer 1

1. Amount from the school board = 608.69

Amount from the chamber = 521.74

2. There are 30 groups of PBPBP

and 10 groups of PPB

Explanation:

1. The project makes 2000 dollars total

total = amount raised + percent from school board * amount raised + percent from chamber * amount raised

We know the total =2000 and the percent from the school board = 70% = .7 and the percent from the chamber = 60% = .6

2000 = amount raised + .70 * amount raised + .60 * amount raised

Factor out the amount raise

2000 = amount raised (1+.7+.6)

2000 = amount raised (2.3)

Divide by 2.3

2000/(2.3) = amount raised

869.56 = amount raised

Amount from the school board =percent from school board * amount raised

=.7 * 869.56

= 608.69

Amount from the chamber =percent from chamber * amount raised

=.6 * 869.56

= 521.74

2. Since each group has 2 P's, the deciding factor is the B's

There are 80 PEP band members

80/2 = 40

So there will be 40 groups

Now we have 1 group with 3 B's and 1 group with 1 B

We have to split 100 B's into those groups

and there are 40 groups

Call the group with 3 B's x and the group with 1 B y

x+y = 40 We need 40 groups

3x + 1y = 100 and we have 100 students to put in those group 3 in the x group and 1 in the y group

2 equations and 2 unknowns

x+y = 40

3x + 1y = 100

Multiply the first equation by -1 sol we can eliminate y

3x + y = 100

-x-y = -40

---------------------

2x= 60

Divide by 2

x = 30

There are 30 groups of PBPBP

x+y = 40

30 +y =40

y =10

and 10 groups of PPB