Answer:
just substitute x for 5 and then solve and then substitute x for -1 and solve and subtract the two answers you get
Answer:
4 mi/h
Step-by-step explanation:
The distance between the cyclists is the hypotenuse of an isosceles right triangle. The hypotenuse is √2 times the length of the legs in such a triangle, so each cyclist must have ridden 8 miles in 2 hours.
Their speed is (8 mi)/(2 h) = 4 mi/h.
_____
<em>Additional comment</em>
Consider an isosceles right triangle with leg lengths 1. Then the Pythagorean theorem tells us the length of the hypotenuse is ...
c² = a² +b² . . . square of hypotenuse is sum of squares of legs
c² = 1² +1² . . . . both legs are 1 in our example triangle
c² = 2
c = √2
That is, the hypotenuse is √2 times the leg length.
Train A will take 2 more hours than train B. Train A will take 5 hours while train B will only take 3 hours.
Let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:
2p + 3d = 18.25
4p + 2d = 27.50
From this, we can use substitution or elimination to solve:
For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.
For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.
I'll be using elimination in this case:
-2(2p + 3d = 18.25) --> -4p - 6d = -36.50
-4p - 6d = -36.50
4p + 2d = 27.50
-4d = -9.00
d = 2.25
4p + 2 * 2.25 = 27.50
4p + 4.50 = 27.50
4p = 23.00
p = 5.75
Now let's check our answer:
2 * 5.75 + 3 * 2.25 = 18.25
11.50 + 6.75 = 18.25
18.25 = 18.25
So drinks cost $2.25 and popcorn $5.75
There were 40 tourist class passengers and 12 first class passengers.
Explanation:
Let the number of passengers who booked for tourist class be
=
x
Then, number of passengers who booked for first class
=
52
−
x
According to question,
Total money paid = $25(tourist class)+$30(first class)
$
1360
=
$
25
(
x
)
+
$
30
(
52
−
x
)
1360
=
25
x
+
1560
−
30
x
1360
−
1560
=
25
x
−
30
x
−
200
=
−
5
x
x
=
−
200
−
5
x
=
40
So, there were 40 tourist class passengers.
Now first class passengers
=
52
−
x
=
52
−
40
=
12
∴
There were 40 tourist class passengers and 12 first class passengers.
As a check
Total money paid = $25(tourist class)+$30(first class)
R
H
S
=
$
25
(
40
)
+
$
30
(
12
)
$
1000
+
$
360
=
$
1360
L
H
S
=
$
1360
Hence verified.
