Find the cost of one large pizza and the cost of one order of bread sticks?

Question

keisha bought three large pizzas and two orders of garlic bread for $26.75. Donna bought four large pizzas and four orders of garlic bread for $39.00.

Answer 1

This is a case of two equations, two unknowns.

 

1st Equation comes from Keisha:

 

3*(large pizza cost) + 2*(garlic bread cost) = $26.75

 

2nd Equation comes from Donna:

4*(large pizza cost) + 4*(garlic bread cost) = $39.00

 

 

Since the second equation has equal parts of unknowns it will be easier to solve for an unknown.

 

Also - first solve for the unknown that you DO NOT want to know.

 

so Donna's Equation:

4*(large pizza cost) + 4*(garlic bread cost) = $39.00

 

simplifies to this equation: (garlic bread cost) = ($39.00 - 4*(large pizza cost)) / 4

 

substitute that into Keisha's equation:

 

3*(large pizza cost) + 2 * (($39.00 - 4*(large pizzas cost)) / 4) = $26.75

 

Solve for cost of a large pizza:

 

3*(large pizza cost) + (2*$39.00 - 2*4*(large pizza cost)) / 4 = $26.75

(SIMPLIFY)

3*(large pizza cost) + ($78.00 - 8*(large pizza cost)) / 4 = $26.75

(SIMPLIFY)

3*(large pizza cost) + ($78.00/4) - 8*(large pizza cost)/4 = $26.75

(SIMPLIFY)
3*(large pizza cost) + $19.50 - 2*(large pizza cost) = $26.75

(SIMPLIFY)
3*(large pizza cost) - 2*(large pizza cost) = $26.75 - $19.50

(SIMPLIFY)
1*(large pizza cost) = $7.25, what a deal!

 

Let's check it w/ the original formulas: 

 

1st Equation comes from Keisha:
3*(large pizza cost) + 2*(garlic bread cost) = $26.75

3*($7.25) + 2*(garlic bread cost) = $26.75

Simplifies to:

(garlic bread cost) = $2.50

 

2nd Equation comes from Donna:
4*(large pizza cost) + 4*(garlic bread cost) = $39.00

4*($7.25) + 4*(garlic bread cost) = $39.00

Simplifies to:

(garlic bread cost) = $2.50 - It checks out.