Question

Start of Questions The admission fee at an amusement park is $5.00 for children and $6.00 for adults. On a certain day, 314 people entered the park, and the admission fees collected totaled $1,740.00 dollars. How many children and how many adults were admitted?

Answer 1

Answer: 144 children and 170 adults were admitted.

Step-by-step explanation:

Let x represent the number of children that were admitted.

Let y represent the number of adult that were admitted.

On a certain day, 314 people entered the park. This means that

x + y = 314

The admission fee at an amusement park is $5.00 for children and $6.00 for adults. The admission fees collected totaled $1,740.00 dollars. This means that

5x + 6y = 1740 - - - - - - - - - - - - -1

Substituting x = 314 - y into equation 1, it becomes

5(314 - y) + 6y = 1740

1570 - 5y + 6y = 1740

- 5y + 6y = 1740 - 1570

y = 170

x = 314 - y = 314 - 170

x = 144

Answer 2

Answer:

144 children and 170 adults

Step-by-step explanation:

make 2 equations

make :

the children as the regarded as the variable : x

the adults are the regarded as the variable  : y

5x + 6 y = 1740

x + y = 314

solve this by the method of elimination

5x + 6y = 1740

5(x + y = 314)

= 5x + 5y = 1570

5x + 6y = 1740

5x + 5y = 1570

the 5x is cancelled out

6y - 5y = 1740 - 1570

y = 170

now replace the value of y in the eqaution

5x + 6 (170) = 1740

5x =720

x = 144

hence they were 144 children and 170 adults

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