You have $33 to spend on 24 balloons. Birthday balloons cost $1.50 each, congratulation balloons cost $1.00 each, and get well balloons
cost $2.00. You want twice as many birthday balloons as the other
two kinds combined. Write and solve a system of equations to find
how many of each type you should buy.

1.5b + 1.0c + 2.0g = 33

b + c + g = 24

[ b = 2(c + g) ]

b - 2c - 2g = 0

(1.5 ... 1.0 ... 2.0 ... ) ( b ) ... (33)

(1 1 1 ) ( c ) = (24)

(1 -2 -2 ) ( g ) ... (0)

(1.5 ... 1.0 ... 2.0 ... ) ( b ) ... (33)

(1 1 1 ) ( c ) = (24)

(3 0 0 ) ( g ) ... (48)

(0 1.0 ... 2.0 ... ) ( b ) ... (9)

(0 1 1 ) ( c ) = (8)

(3 0 0 ) ( g ) ... (48)

(0  0 1 ) ( b ) ... (1)

(0 1 1 ) ( c ) = (8)

(1 0 0 ) ( g ) ... (16)

(0  0 1 ) ( b ) ... (1)

(0 1 0 ) ( c ) = (7)

(1 0 0 ) ( g ) ... (16)

g = 1

c = 7

b = 16

table 1

step-by-step explanation:

1-16

2-32

4-64

8-128

all multiples of 16