SOLUTION: Tanisha and Rachel had lunch at the mall. Tanisha ordered three slices of pizza and two colas.Rachel ordered two slices of pizza and three colas.Tanisha's bill was $6.00, and Rache

Algebra ->  Equations -> SOLUTION: Tanisha and Rachel had lunch at the mall. Tanisha ordered three slices of pizza and two colas.Rachel ordered two slices of pizza and three colas.Tanisha's bill was $6.00, and Rache      Log On


   

Question 719846: Tanisha and Rachel had lunch at the mall. Tanisha ordered three slices of pizza and two colas.Rachel ordered two slices of pizza and three colas.Tanisha's bill was $6.00, and Rachel's bill was $5.25. What was the price of one slice of pizza? What was the price of one cola? Show your steps.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the price in dollars of a slice of pizza
Let +b+ = the price in dollars of a cola
given:
Tanisha's bill:
(1) +3a+%2B+2b+=+6+
Rachel's bill:
(2) +2a+%2B+3b+=+5.25+
---------------------
Multiply both sides of (1) by +3+
Multiply both sides of (2) by +2+
Subtract (2) from (1)
(1) +9a+%2B+6b+=+18+
(2) +-4a+-+6b+=+10.5+
+5a+=+7.5+
+a+=+1.5+
Plug this result back into (1) or (2)
(1) +3%2A1.5+%2B+2b+=+6+
(1) +4.5+%2B+2b+=+6+
(1) +2b+=+1.5+
(1) +b+=+.75+
$1.50 = the price of a slice of pizza
$.75 = the price of a cola
check:
(1) +3a+%2B+2b+=+6+
(1) +3%2A1.5+%2B+2%2A.75+=+6+
(1) +4.5+%2B+1.5+=+6+
(1) +6+=+6+
OK