Answer:
me too
Step-by-step explanation:
Answer:
number of adults tickets sold = x = 90
number of teachers tickets = y = 45
number of students tickets = z = 145
Step-by-step explanation:
Cost of tickets
Adults = $6
Teachers = $4
Students = $2
Total tickets sold = 280
Total revenue = $1010
Let
x = number of adults tickets
y = number of teachers tickets
z = number of students tickets
x + y + z = 280
6x + 4y + 2z = 1010
If the number of adult tickets sold was twice the number of teacher tickets
x = 2y
Substitute x=2y into the equations
x + y + z = 280
6x + 4y + 2z = 1010
2y + y + z = 280
6(2y) + 4y + 2z = 1010
3y + z = 280
12y + 4y + 2z = 1010
3y + z = 280 (1)
16y + 2z = 1010 (2)
Multiply (1) by 2
6y + 2z = 560 (3)
16y + 2z = 1010
Subtract (3) from (2)
16y - 6y = 1010 - 560
10y = 450
Divide both sides by 10
y = 450/10
= 45
y = 45
Substitute y=45 into (1)
3y + z = 280
3(45) + z = 280
135 + z = 280
z = 280 - 135
= 145
z = 145
Substitute the values of y and z into
x + y + z = 280
x + 45 + 145 = 280
x + 190 = 280
x = 280 - 190
= 90
x = 90
Therefore,
number of adults tickets sold = x = 90
number of teachers tickets = y = 45
number of students tickets = z = 145
L = pounds of lollipop
c = pounds of caramel candies
0.95l + 1.10c = 30 ($0.95/lb & $1.10/lb)
l + c = 30 (mixture sells for $1/lb)
c = 30 - l
0.95l + 1.10(30 - l) = 30 (Substitution)
0.95l + 33 - 1.10l = 30
-0.15l = -3 (move terms)
l = 20lbs
Hope this helps.
One number (a) exceeds another number (b) by 11 so
a = b+11
a + b = 77
Substitute the equation for a into the second equation
(b+11) + b = 77
multiply each side by 1 to remove parentheses
b + 11 + b = 77
Combine like terms
2b + 11 = 77
Isolate the variable
2b = 77-11
Simplify
2b = 66
Divide by 2
b = 33
Now substitute b back into the initial equation for a
a = (33) + 11
a = 44
Check your work by substituting both values into the second equation
44 + 33 = 77
This is true, so 44 and 33 are solutions
<h3>
Answer:</h3>
33
<h3>
Step-by-step explanation:</h3>
Vocabulary
Before going into an explanation, let's go over some important vocabulary.
- Collinear - Collinear describes points that are on the same line. This means that there is 1 line with the 3 points L, M, and N.
- Segment addition postulate - The segment addition postulate states that if there are 2 collinear points (A and C) with another point in between them (B), then the statement AB + BC = AC must be true.
Solving for MN
Using the postulate above we can make a new equation. First, let's set up an equation that mirrors the postulate.
Now, let's plug in the values we know.
Then, solve.
This proves that a possible value of MN is 33.
