Meredith is playing games at an arcade to earn tickets that she can exchange for a prize. She has 250 tickets from a previous visit, and she earns 6 tickets for each game she plays. In the equation below, x represents the number of games Meredith plays, and y represents the number of tickets she needs for the prize. y = 6x + 250 If Meredith needs 322 tickets to exchange for the prize she wants, how many games does Meredith need to play?

An equation in mathematics is defined as an equality established between two expressions, in which there may be one or more unknown values, called unknowns, in addition to certain known data.

The unknown or unknowns represent the number (or numbers), if any, that make the equality true. This unknown number or numbers represent the solution of the equation. So when changing the unknown or unknowns by the solution, the equality must be true.

Solution in this case

Meredith is playing games at an arcade to earn tickets that she can exchange for a prize. This is represented by:

y=6x + 250

where:

x represents the number of games Meredith plays.
y represents the number of tickets she needs for the prize.

Meredith needs 322 tickets to exchange for the prize she wants. This is, y=322.

Replacing in the expression y=6x + 250:

322= 6x + 250

Solving taking into account that:

When a value you are adding is passed to another side of the equation, this value will be subtracting.
If a value is multiplying it goes to the other side of the equation by dividing.

322 - 250=6x

72= 6x

72÷6= x

12= x

Finally, the number of games Meredith need to play is 12.

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