SOLUTION: On Tuesday, Wendy picked up three doughnuts and four large coffees for the backroom staff; she paid $4.91. On Thursday Bruce picked up five doughnuts and six large coffees for the

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Question 578644: On Tuesday, Wendy picked up three doughnuts and four large coffees for the backroom staff; she paid $4.91. On Thursday Bruce picked up five doughnuts and six large coffees for the same group; he paid $7.59. What the cost of one doughnut, and of one large coffee?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = cost of 1 donut
Let +b+ = cost of 1 lg coffee
given:
(1) +3a+%2B+4b+=+491+ ( in cents )
(2) +5a+%2B+6b+=+759+ ( in cents )
Multiply both sides of (1) by +5+
Multiply both sides of (2) by +3+
and subtract (2) from (1)
(1) +15a+%2B+20b+=+2455+
(2) +-15a+-+18b+=+-+2277+
+2b+=+178+
+b+=+89+
Plug this back into (1)
(1) +3a+%2B+4%2A89+=+491+
(1) +3a+=+491+-+356+
(1) +3a+=+135+
(1) +a+=+45+
One donut costs 45 cents
One lg coffee cost 89 cents
check:
(2) +5%2A45+%2B+6%2A89+=+759+
(2) +225+%2B+534+=+759+
(2) +759+=+759+
OK