We are asked to find the numbers of children and adults that swam at a public pool on a certain hot day. To do that, we will first try to create a using the given information. Let's call the number of adults at the pool a and the number of children c.
&a← Number of adults at the swimming pool
&c← Number of children at the swimming pool
We are told that that 481 people swam at the public pool that day. This means that the sum of the numbers of adults a and children c is equal to 481.
a+c=481Also, we are told that the daily prices are $1.25 for children and $2.25 for adults. Thus, the income from the tickets for children is $1.25* c and the income from the adult tickets is $2.25* a. The receipts for admission totaled $865.25. Therefore, the sum of $1.25* c and $2.25* a should be equal to $865.25.
1.25* c+ 2.25* a= 865.25
We created two equations for a and c! Together they form a system of equations.
a+c=481 & (I) 1.25c+2.25a=865.25 & (II)
We can solve this system using . Let's begin by isolating a in the first equation.
a+c=481 1.25c+2.25a=865.25
a+c-c=481-c 1.25c+2.25a=865.25
a=481-c 1.25c+2.25a=865.25
Now, we can substitute a=481-c into the second equation.
a=481-c 1.25c+2.25a=865.25
a=481-c 1.25c+2.25( 481-c)=865.25
a=481-c 1.25c+2.25(481)-2.25(c)=865.25
a=481-c 1.25c+1082.25-2.25c=865.25
a=481-c 1.25c+1082.25-1082.25-2.25c=865.25-1082.25
a=481-c - c=- 217
a=481-c c=217
Great! We found that c=217. Now, to find the value of a we can substitute for c into the first equation.
a=481-c c=217
a=481- 217 c=217
a=264 c=217
We found that a=264 and that c=217. This means that 264 adults and 217 children were at the public swimming pool that day.
