There are 150 adults and 225 children at a zoo. If the zoo makes a total of $5100 from the entrance fees, and the cost of an adult and a child to attend is $31 dollars, how much does it cost each
for a parent and a child?

It costs $25 for a parent and $6 for a child

Step-by-step explanation:

Let x be the cost it takes for an adult to enter, and y be the cost it takes for a child to enter then...

x+y=31

150x+225y=5100

We can write the first equation in terms of x by subtracting y from both sides...

x=31-y

Now, we can solve the system of equations by substitution (substitute 31-y for x)...

150(31-y)+225y=5100

Distribute the 150 to the terms inside of the parentheses

150(31)-150(y)+225y=5100

   4650-150y+225y=5100

Combine like terms

4650+75y=5100

Subtract 4650 from both sides

75y=450

Divide both sides by 75

y=6

Plug 6 back in for y to solve for x:

x=31-y=31-6=25

It costs $25 for a parent and $6 for a child

its a straight line parallel to the time axis

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15