Question

Tyler bought two pieces of pizza and three diet Pepsi for $7.25 Scotty but for pizzas a pizza and diet Pepsi for $8.25 set up a system of equations to determine how much a slice of pizza cost and how much a diet Pepsi cost

Answer 1

The cost of

1 slice of pizza = x = $1.75

1 diet pepsi = y = $1.25

Explanation:

Let us represent:

The cost of

1 slice of pizza = x

1 diet pepsi = y

Tyler bought two pieces of pizza and three diet Pepsi for $7.25

2x + 3y = 7.25.......Equation 1

Scotty but four pizzas and a diet Pepsi for $8.25

4x + y = 8.25......Equation 2

Combining the Equations

2x + 3y = 7.25.......Equation 1

4x + y = 8.25......Equation 2

y = 8.25 - 4x

We substitute 8.25 - 4x for y in Equation 1

2x + 3(8.25 - 4x) = 7.25

2x + 24.75 - 12x = 7.25

Collect like terms

24.75 - 7.25 = 12x - 2x

17.5 = 10x

x = 17.5/10

x = $1.75

Solving for y

y = 8.25 - 4x

y = 8.25 - 4(1.75)

y = 8.25 - 7

y = $1.25

Therefore,

The cost of

1 slice of pizza = x = $1.75

1 diet pepsi = y = $1.25