Playing Cards

Kara has 2 times more cards than Dana. Dana has 4× less than Mary. Together, they have 728 cards. How many cards have each of them?

Correct answer:

K =  208
D =  104
M =  416

Step-by-step explanation:

K=2D D=M/4 728=K+D+M  D(1+2+4)=728 D=7728​=104  K=2⋅D=2⋅104=208  M=728−K−D=728−208−104=416

K=2·D
D= M/4
728 = K+D+M

2D-K = 0
4D-M = 0
D+K+M = 728

Pivot: Row 1 ↔ Row 2
4D-M = 0
2D-K = 0
D+K+M = 728

Row 2 - 2/4 · Row 1 → Row 2
4D-M = 0
-K+0.5M = 0
D+K+M = 728

Row 3 - 1/4 · Row 1 → Row 3
4D-M = 0
-K+0.5M = 0
K+1.25M = 728

Row 3 + Row 2 → Row 3
4D-M = 0
-K+0.5M = 0
1.75M = 728


M = 728/1.75 = 416
K = 0-0.5M/-1 = 0-0.5 · 416/-1 = 208
D = 0+M/4 = 0+416/4 = 104

D = 104
K = 208
M = 416

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