SOLUTION: You have $15.25 in quarters and dimes. You have 103 coins total. How many quarters do you have and how many dimes do you have. Show an equation

Question 736981: You have $15.25 in quarters and dimes. You have 103 coins total. How many quarters do you have and how many dimes do you have. Show an equation
Answer by mbogner(1) (Show Source): You can put this solution on YOUR website!
Let x = number of quarters
Let y = number of dimes
x + y = 103 coins
Also, $.25x + $.10y = $15.25
So, from the first equation y = 103 - x, substituting in the second equation,
$.25x + $.10 * (103 - x) = $15.25
or, $.25x + ($.10 * 103) -.10x = $15.25
or, $.25x - $.10x + $10.30 = $15.25
or, ($.25x - $.10x) + ($10.30 - $10.30) = ($15.25 -$10.30)
or $.15x = $4.95, x = $4.95/$.15 = 33 quarters
hence 33 + y = 103, y = 103 - 33 = 70 dimes
Error checking is a must:
($.25 * 33) + ($.10 * 70) = $8.25 + $7.00 = 15.25, which is correct.
Alternatively, one could start with x = 103 - y, and substitute for x. This works, too.
Alternatively, one could start with $.25x + $.10y = $15.25 and solve for x (x= {15.25-.10y})/.25), or y (y={15.25-.25x}/.10), and substitute these into the first equation x + y - 103. Although perfectly good ways, it can be seen that these add complexity and more opportunities for error.
Alternatively, one could use a guessing method and adjust. Say 50 quarter and 53 dimes. This gives 17.8, need fewer quarters. One could use the midpoint method and try halfway, (0+50)/2 = 25 quarters and (103-25 = 78 dimes), 14.05. Need between 25 and 50 quarters. Eventually one would get 33 quarters and 70 dimes.
Alternatively, one could load a spreadsheet from 1 to 102 in the first column (put 1 in cell a1, = 1 + a1 in cell a2, and copy cell a2 from cell a3 to cell a102). Put = 103 - a1 into cell b1 and copy this formula from cell b2 to cell b102. Tthe first row would be 1 (a1), 102 (b1), the second row would be 2 (a1), 101 (b1), until the last row 102 (a102), 1 (b102)). In the third column set up a formula in c1,=(a1*.25) + (b1*.10),giving 10.45. copy this formula from c2 to c102. Look for 15.25 in this column. Row 33 has 33 (a33, quarters) and 70 (b33, dimes) has 15.25 in c33.

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