A)
Let x represent the cost of 1 student, and y the cost of 1 teacher.
B)
In the first group, there's 25 students and 2 teachers. Their total cost is $97.50
So 25x + 2y = 97.50
In the second group, there's 32 students and 3 teachers. Their total cost is $127
So 32x + 3y = 127
We get the following system of equations:
25x + 2y = 97.50 (1)
32x + 3y = 127 (2)
C)
25x + 2y = 97.50 (1)
32x + 3y = 127 (2)
In equation (1)
25x + 2y = 97.50
25x + 2y - 2y = 97.50 - 2y
25x = 97.50 - 2y
25x / 25 = 97.50/25 - 2y/25
x = 3.9 - (2/25)y
In equation (2), let's replace x by its algebraic value
32x + 3y = 127
32(-2/25y + 3.9) + 3y = 127
11/25y + 124.8 = 127
11/25y + 124.8 - 124.8 = 127 - 124.8
11/25y = 2.2
(11/25y) / (11/25) = 2.2 / (11/25)
y = 5
x = -2/25y + 3.9
x = -2/25 * 5 + 3.9
x = 3.5
So the cost of each student is $3.5, and the cost of each teacher is $5.
Hope this helps! :)
Answer:
d) -2
Step-by-step explanation:
(-1 - 19)/(16 - 6)
-20/10 = -2
The 13 stripes alternate red and white: 7 red and 6 white.
Each of 13 stripes is (39 in. / 13) = 3 in. wide.
4 of the 7 red stripes are 39 in. long. The other 3 are 65 in. long.
The total area (l*w) of the flag is (65 in.)*(39 in.)=2535 sq. in.
The red stripes make up an area (l*w) that is:
4*(area of short stripes) + 3*(area of long stripes)
Red area is 4*(39*3) + 3*(65*3) = 1053 sq in.
The fraction of the flag that is red is:
1053 sq. in. / 2535 sq. in.
