<span>Section A seats = 1500
Section B seats = 4500
Lawn seats = 17000
Let's write a few equations to express what we know.
A = number of seats in section A
B = number of seats in section B
L = number of law seats
"There are three times as many seats in Section B as in Section A"
B = 3A
"all 23,000 seats"
L = 23000 - A - B
L = 23000 - A - 3A
"The revenue from selling all 23,000 seats is $870,000"
870000 = 30L + 55B + 75A
Now let's substitute 3A for B
870000 = 30L + 55(3A) + 75A
And substitute (23000 - A - 3A) = (23000 - 4A) for L
870000 = 30(23000 - 4A) + 55(3A) + 75A
And solve for A
870000 = 30(23000 - 4A) + 55(3A) + 75A
870000 = 690000 - 120A + 165A + 75A
870000 = 690000 + 120A
180000 = 120A
1500 = A
So we know that section A has 1500 seats.
Because of B = 3A = 3*1500 = 4500, section B has 4500 seats.
Finally, L = 23000 - A - B = 23000 - 1500 - 4500 = 17000 seats</span>
Answer:
11. 40.5
12. 84
Step-by-step explanation:
When ever you have percentages, it should be helpful to bear in mind you can express them as multipliers. In this case, it will be helpful.
So, if we let:
a = test score
b = target score
then, using the information given:
a = 1.1b + 1
a = 1.15b - 3
and we get simultaneous equations.
'1.1' and '1.15' are the multipliers that I got using the percentages. Multiplying a value by 1.1 is the equivalent of increasing the value by 10%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the simultaneous equations, we can just solve them now:
There are a number of ways to do this but I will use my preferred method:
Rearrange to express in terms of b:
a = 1.1b + 1
then b = (a - 1)/1.1
a = 1.15b - 3
then b = (a + 3)/1.15
Since they are both equal to b, they are of the same value so we can set them equal to each other and solve for a:
(a - 1)/1.1 = (a + 3)/1.15
1.15 * (a - 1) = 1.1 * (a + 3)
1.15a - 1.15 = 1.1a + 3.3
0.05a = 4.45
a = 89
