A group of 28 people go to an amusement park. The admission fee for adults is $12. The admission fee for children is $10. The group spent $296 to get into the park. How many adults and how many children were in the group

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.