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Shtirlitz [24]
3 years ago
6

HELP!!!!

Mathematics
1 answer:
VashaNatasha [74]3 years ago
5 0

Step 1: Assign variable for the unknown that we need to find.

Let x be the charge/person who are under age 12

Let y be the charge/person who are over age 12, and

Let z be the charge/person who are adults.

Step 2: Based on the information given write mathematical equation

Statement 1: "A family with 2 kids under age 12, 3 kids over age 12, and 3 adults pays $174 for entrance to the park"

For Under Age 12, 1 kid charge $x, so 2 kids under age 12 charge will be $2x.

For Over Age 12, 1 kid charge $y, so 3 Kids over age 12 charge will be $3y.

For Adults, 1 Adult charge $z, so 3 Adults charge will be $3z

Based on the above statement which mentions the number of person in the family and total cost of $174, we can write our 1st equation as

2x + 3y + 3z = 174 ⇒ 1st Equation

Statement 2: "A mother and father bring their 4 kids under age 12 at a cost of $122"

4 kids under 12 will be charged $4x, & 2 Adults (Mother and father) will be charged $2z, and total cost is given as $122.

Based on the above statement 2, we can write the 2nd equation as

4x + 2z = 122 ⇒ 2nd Equation

Statement 3: A grandmother who brings her teenage granddaughter to the park pays $46.

Grandmother will be considered an adult with teenage granddaughter who need to be considered as kid over age 12.

So we can write the third equation as

y + z = 46 ⇒ 3rd equation.

Step 3: Solve the three equation using substitution method

2x + 3y + 3z = 174 ⇒ 1st Equation

4x + 2z = 122 ⇒ 2nd Equation

y + z = 46 ⇒ 3rd equation

Factoring 3 in the left side of the last two terms of 1st equation we get...

2x + 3(y + z) = 174

Then substituting 46 for y + z we get

2x + 3(46) = 174

2x + 138 = 174 { Subtracting 138 on both sides }

2x +138 - 138 = 174 - 138 {Combining like terms on either side of the equation}

2x = 36 {Dividing 2 on both sides}

2x/2 = 36/2 {Simplifying each fraction}

<em>x = 18</em>

Substituting 18 for x in 2nd equation, 4x + 2z = 122

4(18) + 2z = 122

72 + 2z = 122 {Subtracting 72 on both sides of the equation}

72 + 2z - 72 = 122 - 72 {Combining like terms on both sides of the equation}

2z = 50 {Dividing by 2 on both sides}

2z/2 = 50/2 {Simplifying fraction on both sides of equation}

<em>z = 25</em>

Substituting 25 for z in the 3rd equation y + z = 46

y + 25 = 46 { Subtracting 25 on both sides of the equation }

y + 25 - 25 = 46 - 25 {Combining like terms on either side of the equation}

<em>y = 21</em>

Conclusion:

The cost for an Kid who are under age 12 to enter the theme park = $18

The cost for an Kid who are over age 12 to enter the theme park = $21

<u><em>The cost for an adult to enter the theme park = $25</em></u>

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English- If it costs 85 dollars for 3 hours we want to double that to get the amount for 6 hours which is 170 dollars. This is before sales tax. You can find the amount after sales tax by multiplying 170 by 1.07. You do this because 100 percent of the cost would be 170 times 1, and 7 percent is .07, so if you want 107 percent of the cost you want to do 170 times 1.07. This works because it takes 7 percent of 170 and adds it to the total cost. You could also do this by 170 times .07. Then add the product to 170. 181.9 is the final answer.

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The graph of the equations is also attached with the answer below.

Therefore the solution of the linear equations will be ( -2, 4).

The complete question is given below:-

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