Question 1181953
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Here is a different path to the solution.  Not the most efficient path; but if you are good with mental arithmetic this method can allow you to solve the problem mentally.<br>
Given:
2 cups of coffee and 3 muffins cost $11.25 : 2x+3y=11.25 [1]
1 cup of coffee and 2 muffins cost $6.87 : x+2y=6.87 [2]<br>
Comparing those two purchases tells us<br>
1 cup of coffee and 1 muffin cost $11.25-$6.87 = $4.38 : x+y=4.38 [3]<br>
Now use elimination using [2] and [3]: multiply [3] by -1 and add to [2] to give<br>
y=6.87-4.38=2.49 [4]<br>
Then use [3] and [4] to find x=4.38-2.49=1.89<br>
ANSWERS: coffee x=$1.89; muffin y=$2.49<br>
Mentally, the solution goes something like this:<br>
2 coffees and 3 muffins cost $11.25
1 coffee and 2 muffins cost $6.87
So 1 less coffee and 1 less muffin costs $11.25=$6.87=$4.38 less
Taking away 1 coffee and 1 muffin again leaves one muffin, at a cost of $6.87-$4.38=$2.49
Then the cost of the coffee is $4.38-$2.49=$1.89<br>