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The admission fee at an amusement park is $3.75 for children and $6.40 for adults.

The admission fee at an amusement park is $3.75 for children and $6.40 for adults. On a certain day, 295 people entered the park, and the admission fees collected totaled 1464 dollars. How many children and how many adults were admitted?

number of children equals
number of adults equals

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This is a repeat of a question that I just answered.

 

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1 Answer

Hi Treena,

Let us assume that the number of children who entered the park is x.

Now, we know that 295 people entered the park on a certain day. Which means the number of adults who entered the park is (295 - x). You want to interpret this as, off the 295 people who entered the park on a given day, we know that x of them were children. Therefore, the balance must be adults.

Therefore, we have

Number of children who entered the park = x

Number of adults who entered the park = 295 - x

The fee for children is $3.75 and for adults is $6.40.

Therefore, total amount that x children paid to enter the park is $3.75 * x

and, total amount that adults paid to enter the park is $6.40 * (295 - x) = 1888 - 6.40 * x.

Therefore, combining the two amounts we will have the total admission fees collected. That is,

(Total amount paid by children) + (Total amount paid by adults) = Total admission fees collected.

Putting our numbers,

(3.75 * x) + (1888 - 6.40 * x) = 1464. 

The expression on the left hand side will simplify to 1888 - (6.40 * x) + (3.75 * x). Combining the x term coefficients we have -6.40 + 3.75 = 2.65.

The expression on the left hand side simplifies to 1888 - 2.65 * x and is equal to 1464.

That is, 1888 - 2.65 * x  = 1464. Let us move the 1464 to the left hand side and move the 2.65 * x term to the right. Since we are moving them to opposite sides of the equation, each term will reverse sign.

Therefore, now 1888 - 1464 = 2.65 * x. Or, 424 = 2.65*x.

Dividing both sides by 2.65, gives us (424 / 2.65) = (2.65 / 2.65)*x

Or, 160 = x. Therefore, 160 children entered the park. And (295 - x) adults entered the park - or, (295 - 160)  adults - which is 135 adults.

Therefore, number of children = 160 and number of adults = 135

I hope this helps