SOLUTION: On Monday, Luis picked up seven scones and four large coffees for the office staff. He paid $25.29. On Tuesday, Rachael picked up two scones and five large coffees for the office a

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Question 1060507: On Monday, Luis picked up seven scones and four large coffees for the office staff. He paid $25.29. On Tuesday, Rachael picked up two scones and five large coffees for the office and staff. She paid $14.13. What is the cost of one scone? What is the cost of one large coffee?
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
7a+4b = 25.29 multiply all sides times 2
2a+5b = 14.13 multiply all sides times 7 and subtract from new equation above
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New equations:
14a+8b = 50.58
-
14a+35b = 98.91
0a+-27b = -48.33
Now we have:
-27b = -48.33
b = -48.33/-27 = 1.79 is the cost of one large coffee.
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For practice (your practice, so you copy what I do and learn):
7a+4b = 25.29 multiply all sides times 5
2a+5b = 14.13 multiply all sides times -4 and ADD to the new equation above
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New equations:
35a+20b = 126.45
+
-8a-20b = -56.52
27a-0b = 69.93
Now we have:
27a = 69.93
a = 2.59 is the price of each scone
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
Check (I'll do one, you can do the other)
7a+4b = 25.29
7(2.59)+4(1.79) = 25.29 Use your calculator and you'll find that it is correct.
:
John