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please help!!!!


On a certain hot summer's day, 554 people used the public swimming pool. The
daily prices are $1.75 for children and $2.50 for adults. The receipts for admission totaled $1097.00.
How many children and how many adults swam at the public pool that day?

Respuesta :

Answer:

Children= 384      Adults= 170

Step-by-step explanation:

First, write a system of algebraic equations:

[tex]1.75x+2.50y=1097[/tex]

[tex]x+y=554[/tex]

Second, use linear combination to eliminate one variable (I will eliminate x, or children.)

[tex]1.75x+2.50y=1097[/tex]

[tex]-1.75(x+y=554)[/tex]

[tex]1.75x+2.50y=1097[/tex]

[tex]-1.75x+-1.75y=-969.5[/tex]

[tex]0.75y=127.5[/tex]

Divide both sides by 0.75

[tex]0.75y=127.5[/tex]

[tex]/0.75[/tex]        [tex]/0.75[/tex]

[tex]y=170[/tex], there are 170 adults

Now, plug in 170 for [tex]x+y=554[/tex]

[tex]x+170=554[/tex]

Subtract 170 from both sides

[tex]x+170=554[/tex]

      [tex]-170[/tex]   [tex]-170[/tex]

[tex]x=384[/tex], there are 384 kids.

Hope this helps!!!

Answer:

384 children and 170 adults

Step-by-step explanation:

if x is children and y is adults

1.75x+2.5y=1097

x+y=554

1.75x=1097-2.5y

x=554-y

1.75x=1097-2.5y

1.75x=1.75(554-y)

1097-2.5y=969.5-1.75y

1097-969.5=2.5y-1.75y

127.5=0.75y

127.5/0.75=y

170=y

x+y=554

x=554-y

x=554-170

x=384

to prove these are correct just do 1.75(384)+2.5(170) and see if it equals 1097, and do 384+170 to see if its the amount of people

1.75(384)+2.5(170)

672+425

1097

384+170=554

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