Systems of Linear Equations

Real-World Problems

Block 45

System of Linear Equations

The admission fee at a school fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

System of Linear Equations

Many problems lend themselves to being solved with systems of linear equations.

In real life, these problems can be incredibly complex.

System of Linear Equations

This is one reason why using linear systems is one way to solve these type problems.

Example #1: The admission fee at a school fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

System of Linear Equations

The admission fee at a school fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

C + A = 2200

System of Linear Equations

The admission fee at a school fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

1.5C +4.0 A = 5050

System of Linear EquationsThe admission fee at a school fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

C + A = 22001.5C +4.0 A = 5050

System of Linear Equations

C + A = 22001.5C +4.0 A = 5050

System of Linear Equations

Example #2: The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

T + U = 7

System of Linear Equations

Example #2: The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

TU is number – written as 10T + U UT is number reversed – written as 10U + T

System of Linear Equations

Example #2: The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

T + U = 7Digits reversed # increased by 27

10U+T = 10T+U+27

System of Linear Equations

Example #2: The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

T + U = 710U+T = 10T+U+27

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