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Sam has exactly 18.90 in dimes and quarters, with an equal number of dimes and quarters.  He spends five quarters and twice as many dimes at the convenience store, and he spends 55 cents at the donut shop.  If he pays the exact amount for everything, how many quarters does Sam have left?

 Jul 15, 2022
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Q==Quarters,   D==Dimes

 

Q == D.........................................................................................(1)

0.55 ==3D + 1Q

[5Q + 1Q] =6 quarters already spent

[3D + 10D]==13 Dimes already spent

 

[6Q x 0.25] + [13D x 0.10] ==$2.80 already spent.

 

0.25[Q - 6] + 0.10[D - 13] ==18.90 - 2.80==16.10....................(2), solve for D, Q

 

D==54 Dimes

Q==54 Quarters that Sam started with

 

54 Dimes  -  13 dimes ==41 Dimes Sam has left.

54 Qurters   -  6 Quartes ==48 Quarters Sam has left

 Jul 15, 2022

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