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

Verified Answer :

Amberruth

y+x=31, 150x+225y=5100. 
y=-x+31
150x+225(-x+31)=5100
-75x=-1875
x=25 (adult tickets are $25)
31-25= 6 (child tickets are $6)

Answer:

The entrance fee per parent is $25, while the cost per child is $6.

Step-by-step explanation:

This problem is solved by using a system of equations.

We know that there are 150 adults and 225 children, which makes a total of $5100. So, the variables here will represent the cost per adult and the cost per children. The first equation is

@@MATH_TOKEN_0@@

Where @@MATH_TOKEN_1@@ represents the cost per adult and @@MATH_TOKEN_2@@ represents the cost per child.

We also know that the entrance fee of an adult and a child is $31, this means

\(x+y=31\)

Now, we isolate \(x\) in the second equation, to replace it into the first equation and solve for \(y\), as follows

\(x+y=31\\x=31-y\)

Then,

\(150x+225y=5100\\150(31-y)+225y=5100\\4650-150y+225y=5100\\75y=5100-4650\\y=\frac{450}{75}=6\)

Now, we use this value to find the other one

\(x+y=31\\x+6=31\\x=31-6=25\)

Therefore, the entrance fee per parent is $25, while the cost per child is $6.

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