Answer: This is a systems of equations problem!
Let's first set up our system by assigning x and y to mean something. Let x = number of children and y = number of adults.
First equation: Children cost $1.50 and Adults cost $4.00. In order to find the amount of money a group of children will cost, we multiply the number of children, x, by 1.5. This is represented by 1.5x. For adults, who cost 4 dollars to enter, we will use 4y. The total amount of money made on the given day was $862. To get this amount, we must add 1.5x and 4y.
1.5x + 4y = 862 works for the money equation involved.
Second equation: Total amount of people on the given day is 283. To get this number, we must add together x and y, or the number of children and adults.
x + y = 283
System of equations:
1.5x + 4y = 862
x + y = 283
Let's use substitution of the x variable to solve the system.
x + y = 283 <--- subtract x from both sides
y = 283 - x
Substitute y = 283 - x into the first equation.
1.5x + 4 (283 - x) = 862 <--- distribute 4 to 283 and -x
1.5x + 1132 - 4x = 862 <--- combine 1.5x and -4x
1132 - 2.5x = 862 <--- subtract 1132 from both sides
-2.5x = -270 <--- divide both sides by -2.5
x = 108
Substitute x =108 back into y = 283 - x
y = 283 - 108 = 175
There were 108 children and 175 adults.
Step-by-step explanation:
