Answer:
1) either 5 or 6 students in the group
2) 6 rooms are booked
Step-by-step explanation:
1) x students
3x + 8 = apples
5 (x-1) + y (the one get less than 5 apples)
3x + 8 = 5 (x - 1) + y
3x + 8 = 5x - 5 + y
2x + y = 13
X 1 2 3 4 5 6
Y 11 9 7 5 3 1
because y < 5 so x = 5 or x = 6
2) x rooms are booked
4x + 20 total students
8 (x-1) + y (the students in room not full))
4x + 20 = 8 (x-1) + y
4x + 20 = 8x - 8 + y
4x + y = 28
X 1 2 3 4 5 6
Y 24 20 16 12 8 4
y < 8 answer is 6 rooms
Answer:
Step-by-step explanation:
N is between points M and O
MN = x
MO = 3x - 6
NO = x + 1
The way it reads MN + NO = MO
x + x + 1 = 3x - 6
2x + 1 = 3x - 6
2x - 2x +1 = 3x -2x - 6
1 = x - 6
1 + 6 = x
x = 7
MO = 3x - 6
MO = 3*7 - 6
MO = 21 - 6
MO = 15
First you need to simplify the left side of the equation to get
Then you add by two on both sides to get
Finally you divide by 2 on both sides to get
Total of 90 fish:
c + p = 90
Charlie gave 1/4 c to Peter. Now
Charlie has c - (1/4) c
Peter has p + (1/4) c
Peter gave 2/5 of his to Charlie. Now
Peter has p + (1/4) c - 2/5( p + (1/4) c )
Charlie has c - (1/4) c + 2/5( p + (1/4) c )
And then they had equal number:
c - (1/4) c + 2/5( p + (1/4) c ) = p + (1/4) c - 2/5( p + (1/4) c )
Let's do the easy subtractions then multiply by 20 to clear the fractions,
(3/4) c + 2/5( p + (1/4) c ) = 3/5( p + (1/4) c )
15c + 8p + 2c = 12p + 3c
14c = 4p
7c = 2p
c + p = 90
2c + 2p = 180
2c + 7c = 180
9c = 180
c = 20
p = 70
Answer: Charlie started with 20, Peter with 70
Check:
Initially C:20, P:70
1/4(20)=5 to P
C:15, P:75
(2/5) 75 = 30 to C
C:45, P45
Good
