the admission fee at an amusement park is $1.25 for children and $6.80 for adults. on a certain day, 356 people entered the park, and the admission fees collected totaled $1333. how many children and how many adults were admitted?

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19-12-2022
Mathematics

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the admission fee at an amusement park is $1.25 for children and $6.80 for adults. on a certain day, 356 people entered the park, and the admission fees collected totaled $1333. how many children and how many adults were admitted?

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-22T00:51:35-05:00

The number of children that were admitted = 196

The number of adults that were admitted = 160

Given that,

The admission fee at an amusement park for children = $1.25

The admission fee at an amusement park for adults = $6.80

On a certain day, people entered the park = 356

The admission fees collected totaled = $1333

Let us assume,

The number of children that were admitted represented as = x

The number of adults that were admitted represented as = y

On a certain day, 356 people entered the park.

So,

We can write,

x + y = 356

x = 356 - y (Equation-1)

The admission fee at the amusement park is $1.25 for children and $6.80 for adults.

The admission fees collected on that day totaled $1333.

Then the,

1.25x + 6.8y = 1333 (Equation-2)

Substituting x = 356 - y into equation 2, it becomes

1.25x + 6.8y = 1333

1.25(356 - y) + 6.8y = 1333

445 - 1.25y + 6.8y = 1333

-1.25y + 6.8y = 1333 - 445

5.55y = 888

y = 888 / 5.55

y = 160

Then we can substitute y value in equation - 1,

x = 356 - y

x = 356 - 160

x = 196

Therefore,

The number of children that were admitted = 196

The number of adults that were admitted = 160

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