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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

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

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