Answered

the cost is admission to the Spring Carnival was $50 for a group of 9 children and 2 adults. The admission was $61 for another group of 10 children and 3 adults. what was the admission for each child? adults?

Answer :

absor201

The cost of one child ticket is $4 and cost of adult ticket is $7.

Step-by-step explanation:

Let,

Cost of one child ticket = x

Cost of one adult ticket = y

According to given statement;

9x+2y=50      Eqn 1

10x+3y=61      Eqn 2

Multiplying Eqn 1 by 3

[tex]3(9x+2y=50)\\27x+6y=150\ \ \ Eqn\ 3[/tex]

Multiplying Eqn 2 by 2

[tex]2(10x+3y=61)\\20x+6y=122\ \ \ Eqn\ 4[/tex]

Subtracting Eqn 4 from Eqn 3

[tex](27x+6y)-(20x+6y)=150-122\\27x+6y-20x-6y=28\\7x=28[/tex]

Dividing both sides by 7

[tex]\frac{7x}{7}=\frac{28}{7}\\x=4[/tex]

Putting x=4 in Eqn 1

[tex]9(4)+2y=50\\36+2y=50\\2y=50-36\\2y=14\\[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{14}{2}\\y=7[/tex]

The cost of one child ticket is $4 and cost of adult ticket is $7.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/726990
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