Admission Fees The admission fee at an amusement park is ...

Admission Fees The admission fee at an amusement park is $\$ 1.50$ for children and $\$ 4.00$ for adults. On a certain day, 2200 people entered the park, and the admission fees that were collected totaled $\$ 5050 .$ How many children and how
many adults were admitted?

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Key Concepts

Elimination/Substitution Methods

These are common techniques for solving systems of linear equations. The substitution method involves solving one equation for a variable and then substituting it into another equation, while the elimination method involves adding or subtracting equations to eliminate one of the variables, simplifying the process of finding the solution.

Word Problem Translation

This involves reading a real-world problem and converting the information given into mathematical statements or equations. It requires identifying unknowns and understanding relationships, such as totals or differences which can be represented algebraically.

Systems of Linear Equations

A system of linear equations is a set of equations with multiple variables that are solved simultaneously. In real-world problems, these systems often arise when there are multiple conditions or constraints, such as combining numbers and values to obtain totals.

Transcript

00:01 Okay, so the word problem states the admission fee at an amusement park is $150 for children and $4 for adults.

00:15 On a certain day, 2 ,200 people entered the park and admission fees were collected that totaled $5 ,050.

00:27 How many children and adults were admitted? okay, so we have two variables here, children and adults.

00:36 So let's put x is equal to children, write a number of children, and y is equal to the number of adults.

00:49 And it says that for children, their admission fees are 150 per child.

00:58 We have $4 per adult, and our total admission fees collected.

01:07 Was $5 ,050.

01:12 Okay, they also state that there's 2 ,200 people.

01:17 So we have the number of children plus the number of adults, y is equal to 2 ,200.

01:26 Okay, so this is our system of equations, and now we need to solve for x and y, which is the number of children, and then the number of adults.

01:37 Okay, so let me rewrite that here.

01:38 We have 1 .50 x plus 4 y is equal to 505 .0 and x plus y is equal to 2200.

01:55 Okay.

01:56 Okay.

01:57 So i'm going to work with equation 1 and you see that, i mean we see that equation 2 has our x and y coefficients of 1.

02:09 So let me just solve for y and substitute y into our first equation and solve for x...

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