Question

Here are two stories:

Story 1: A family buys 6 tickets to a show. They also each spend $3 on a snack. They spend $24 on the show.

Story 2: Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends, and then adds 6 more
ounces for each.

Here are two equations:
3(x + 6) = 24
6(x+3) = 24
Which equation represents Story 1?​

Answer 1

The second equation i.e. 6(x + 3) = 24 represents the scenario of Story 1.

Story 1 Scenario :

• Story 1 has 6 family members.
• Each of the members has expenses for food and movie.
• The expense of food for each of the member is given as 3 dollars
• Let us assume the expense of a movie per member be "x" dollars

So, forming the equation :

Total cost = number of members * total cost of each member

                = number of members * ( cost of food + cost of movie ) for each

               

Replacing the equation with numbers :

          $24 = 6(x+3)$

Story 2 Scenario :

• Story 2 has 3 friends or members
• Each of the friends is poured initially an equal amount of liquid and then 6 more ounces
• The additional juice poured into each in the last is 6 ounces.
• Let us assume the initial juice poured be "x" ounces

So, forming the equation :

Total juice = number of friends * total juice distributed to each friend

                = number of friends * ( equal amount + additional ) for each

               

Replacing the equation with numbers :

          $24 = 3(x+6)$

Hence, the equation for Story 1 is the second option i.e. 6(x+3) = 24.

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Answer 2

The equation that represents Story 1 is 3(x+6) = 24.

To understand why, let's break down the story. A family buys 6 tickets to a show, and each person spends $3 on a snack. We can represent the cost of the tickets as 6x, where x is the cost of one ticket. We can also represent the cost of the snacks as 3(6), since there are 6 people each spending $3.

The total cost of the tickets and snacks is 6x + 18. However, we also know that they spent a total of $24 on the show. So, we can set up the equation:

6x + 18 = 24

To solve for x, we can subtract 18 from both sides:

6x = 6

And then divide both sides by 6:

x = 1

So the cost of one ticket is $1.

Now we can plug in the value of x into the expression for the cost of the snacks:

3(6) = 18

So the total cost of the tickets and snacks is:

6(1) + 18 = 24

Therefore, the equation that represents Story 1 is 3(x+6) = 24.

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