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Tickets to the local carnival cost $5.50 for adults and $3.00 for children under the age of 12. A group of 8 people bought tickets to the carnival for $36.50. Write a system of equations to represent this scenario. How many adult tickets were sold?

Respuesta :

calculista

Answer:

The number of adult tickets sold was 5

Step-by-step explanation:

Let

x ----> the number of adult tickets

y ----> the number of child tickets

we know that

[tex]x+y=8[/tex]

isolate the variable y

[tex]y=8-x[/tex] ----> equation A

[tex]5.50x+3y=36.50[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]5.50x+3(8-x)=36.50[/tex]

solve for x

apply distributive property left side

[tex]5.50x+24-3x=36.50[/tex]

combine like terms

[tex]2.50x+24=36.50[/tex]

subtract 24 both sides

[tex]2.50x=36.50-24[/tex]

[tex]2.50x=12.50[/tex]

Divide by 2.50 both sides

[tex]x=5[/tex]

therefore

The number of adult tickets sold was 5

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