SOLUTION: On​ Monday, Luis picked up seven scones and two large coffees for the office staff. He paid $ 22.30. On​ Tuesday, Rachel picked up four scones and five large coffees for the of

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: On​ Monday, Luis picked up seven scones and two large coffees for the office staff. He paid $ 22.30. On​ Tuesday, Rachel picked up four scones and five large coffees for the of      Log On


   



Question 1135386: On​ Monday, Luis picked up seven scones and two large coffees for the office staff. He paid $ 22.30. On​ Tuesday, Rachel picked up four scones and five large coffees for the office staff. She paid $ 20.38. What is the cost of one​ scone? What is the cost of one large​ coffee?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost of 1 scone
Let +b+ = the cost of 1 lg coffee
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(1) +7a+%2B+2b+=+22.3+
(2) +4a+%2B+5b+=+20.38+
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Multiply both sides of (1) by +5+
Multiply both sides of (2) by +2+
Subtract (2) from (1)
(1) +35a+%2B+10b+=+111.5+
(2) +-8a+-+10b+=+-40.76+
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+27a+=+70.74+
+a+=+2.62+
and
(1) +4a+%2B+5b+=+20.38+
(1) +4%2A2.62+%2B+5b+=+20.38+
(1) +10.48+%2B+5b+=+20.38+
(1) +5b+=+9.9+
(1) +b+=+1.98+
One large coffee costs $1.98
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(1) +4%2A2.62+%2B+5%2A1.98+=+20.38+
(1) +10.48+%2B+9.9+=+20.38+
(1) +20.38+=+20.38+
Ok
You can check (2)