Step 1: We need to assign variable for the unknown that we need to find.
Let x be the number of adults in the group who went to an amusement park
and y be the number of children in the group who went to an amusement park.
Step 2: Based on the given statement we need to write mathematical equation.
Statement 1: " group of 28 people go to an amusement park."
Based on the above statement we can write the first equation
x + y = 28 ⇒ 1st Equation
Statement 2: "The admission fee for adults is $12. The admission fee for children is $10. The group spent $296 to get into the park. "
1 adult spent $12 as fee, so ' x ' adults will spend 12x dollars as fee
1 child spent $10 as fee, so ' y ' children will spend 10y dollars as fee.
Totally the group spent $296 to get into the park, so that second equation can be written as
12x + 10y = 296 ⇒ 2nd Equation
Step 3: Solve the equation using substitution method.
Solve the 1st equation for y by subtracting x on both sides, we get y = 28 - x
Then substituting 28 - x for y in the 2nd equation, we get the below equation with one variable (x).
12x + 10(28 - x) = 296 {Distribute 10}
12x + 280 - 10x = 296 {combine like terms}
2x + 280 = 296 {Subtract 280 on both sides of the equation}
2x + 280 - 280 = 296 - 280 {Combine like terms in either side of the equation}
2x = 16 {Divide by 2 on both sides}
2x/2 = 16/2 {Simplify the fractions on both sides}
x = 8.
Substitute 8 for x in the equation x + y = 28 and find the value of y
8 + y = 28 {Subtraction 8 on both sides}
8 + y - 8 = 28 - 8 {Combining like terms}
y = 20
Conclusion:
There were 8 adults and 20 Children in the group who went to an amusement park.
