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The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 235 people entered the park, and the admission fees collected totaled 640 dollars. How many children and how many adults were admitted?

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rspill6

Answer:  115 Adults and 120 Children

Step-by-step explanation:

We have 2 unknowns:  A is the number of Adults and C is the number of children.

We'll need at least two equations to solve for two unknowns.

One equation is easy:  We know that A + C = 235, the total number of people who entered the park.

The second equation comes from the second fact that was provided:  total admission fees were $640.  We can write the sum of the two unknowns, A and C, when multiplied by their respective admission fee:

4A + 1.5C = $640  [$4 * the number of adults plus $1.5 * the number of children]

Rearrange the first equation for either variable, A or C.  I picked A:

A = 235 - C

Now use this value for A in the second equation:

4A + 1.5C = $640

4*(235-C) + 1.5C = $640

-2.5C + 940 = 640

-2.5C = -300

C = 120 children

To find A:

A = 235 - C

A = 235 - 120

A = 115 adults

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Double check to see if these value work:

                    C       A

Fee($)          1.5      4

People        120    115

Income ($)   180   460

Total = 180 + 460 = $640

It works.  120 Adults and 115 Children.