how do you solve word problems?

Question

Brianna`s family bought 2 youth tickets and 3 adult tickets at an amusement park for a total of $134. Max`s family bought 4 youth tickets and 2 adult tickets for a total of $146. Find how much an adult ticket costs and how much a youth ticket costs.

 

Define two variables, write two equations, solve and answer in a sentence.

Answer 1

1. The first thing you need to do is write down the information given to you in the problem.
1. You have 2 youth tickets and 3 adult tickets for $134, and 4 youth tickets and 2 adult tickets for $146.
2. Second, you need to identify the variables.
1. You can choose any variables you like. For this problem lets put youth tickets as y and adult tickets as x.
3. Next, it is time to set up the equations
1. For the first equation
1. 2y+3x=134
2. For the second equation
1. 4y+2x=146
4. Finally, lets solve the equations.
1. There are two main ways to solving a set of equations. The first one is elimination. Through elimination, the first step is to set up the equations this way
1. 2y+3x=134
2. 4y+2x=146

The next step is to set one of the variables equal by multiplying the whole equation by a certain number. In this case, lets multiply equation number 1 by 2 so the variable y can be the same.

1. 4y+6x=268
2. 4y+2x=146

The next step is to either subtract or add (whichever is easier) to eliminate one of the variables. In this case, lets subtract so we can eliminate the y variable.

1. 4y+6x=268

      -(4y+2x=146)

              4x=122

Next, lets solve for x by dividing 8 on both sides

1. 8x=122

         4     4  

         x=30.5

Now that we have x, we can plot in the x value in any of the two original equations (whichever one you like best). In this problem lets pick the second equation. 

1. 4y+2x=146

        4y+2(30.5)=146

        4y+61=146

        4y=85

Finally, lets solve for y.

1. 4y=85
   

         4    4  

        y=21.25

The answer gathered through elimination was that y=21.25 and x=30.5

 

    2. The second way is substitution. For substitution, the first step is to solve one of the equations for one of the         variables. For this problem lets solve equation number 2 for the variable x.

1. 4y+2x=146

       -4y         -4y

             2x=146-4y

             2       2    

        x=73-2y

The next step is to substitute the this equation into the x of equation 1

1. 2y+3x=134

        2y+3(73-2y)=134

        2y+219-6y=134

        219-4y=134

The next step is to solve for y.

1. 219-4y=134

       -219      -219

             -4y=-85

              -4    -4   

              y=21.25

The final step it to substitute the y value into one of the original equations and solve for x. Lets choose the fist equation.

1. 2y+3x=134

        2(21.25)+3x=134

        42.5+3x=134

       -42.5       -42.5

                3x=91.5

                 3     3   

                 x=30.5

 

Through both processes, we got the same answers. The youth tickets are $21.25 each and the adult tickets are $30.50 each. The best way of knowing if your answer is correct is to plug in the answers to the 2 original equations and checking if they are correct.

Answer 2

You solve word problems by taking the given information and translating it into the specified formulas. We need to start by IDing our variables. we'll make y stand for youth tickets and a for adult tickets.

Here's what we know:

2y + 3a = 134 (Brianna's family bought 2 youth & 3 adult for $134)

4y + 2a = 146 (Max's family bough 4 youth and 2 adult for $146)

 

What we now have is a system of equations. I suggest using the elimination method as we have a 2y and 4y that we can quickly remove by multiplying the first equation by -2:

-4y - 6a = -268

4y  + 2a = 146

-------------------

-4a = -122

a = 30.5

 

Now that we know the cost of an adult, we can solve for y and check our answer:

2y + 3 * 30.5 = 134

2y + 91.5 = 134

2y = 42.5

y = 21.25

 

4 * 21.25 + 2 * 30.5 = 146

85 + 61 = 146

146 = 146

 

So adults are $30.50 and youth $21.25.

Answer 3

Let Y = price of Youth ticket and A = price of Adult Ticket

1) 2Y + 3A = 134

2) 4Y + 2A = 146

The second equation can be reduced to

3) 2Y   + A = 73

 

Subtracting 3) from 1) gives

2A = 61

A = $30.5

Solving for Y

Y = $21.25