Answer:
Let's define the variables:
A = price of one adult ticket.
S = price of one student ticket.
We know that:
"On the first day of ticket sales the school sold 1 adult ticket and 6 student tickets for a total of $69."
1*A + 6*S = $69
"The school took in $150 on the second day by selling 7 adult tickets and student tickets"
7*A + 7*S = $150
Then we have a system of equations:
A + 6*S = $69
7*A + 7*S = $150.
To solve this, we should start by isolating one variable in one of the equations, let's isolate A in the first equation:
A = $69 - 6*S
Now let's replace this in the other equation:
7*($69 - 6*S) + 7*S = $150
Now we can solve this for S.
$483 - 42*S + 7*S = $150
$483 - 35*S = $150
$483 - $150 = 35*S
$333 = 35*S
$333/35 = S
$9.51 = S
That we could round to $9.50
That is the price of one student ticket.
When , we have
and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for , that
Now for , we have
so we know the left side is at least divisible by by our assumption.
It remains to show that
which is easily done with Fermat's little theorem. It says
where is prime and is any integer. Then for any positive integer ,
Furthermore,
which goes all the way down to
So, we find that
QED
Hey There! :)
To Solve for t.
Distribute the brackets.
Subtract 7t from both sides.
Factor out variable, t.
Divide both sides by h-7.
Hope this helps!
-Benjamin
The answer is really simple. 3 quarts is more. There are 4 pints in a quart. There are 4 quarts in a gallon.
Answer:
From the given picture we can see that , 3 teaspoons = 1 table spoon.....(1)
or 3t=b..(2)
6 teaspoon= 2 tablespoon or 6t=2b
9 teaspoon= 3 table spoon or 9t=3b
Therefore the ratio of teaspoon to tablespoon t:b= 3:1...........(from (1))
Now, 1 tea spoon=..............[divide 3 on both sides of (1)]
or
The equation to show the relation between teaspoons and table spoon is given by (2)
3t=b