Together 3206

Jana, Martina, and Zuzka shared candies in a ratio of 4:5:3. During this division, Martina had 16 sweets less than Jana and Zuzka had together. How many candies did each of the girls have?

Correct answer:

J =  32
M =  40
Z =  24

Step-by-step explanation:


J=4k
M=5k
Z=3k
M = J+Z-16

J=4·k
M=5·k
Z=3·k
M = J+Z-16

J-4k = 0
M-5k = 0
Z-3k = 0
J-M+Z = 16

Row 4 - Row 1 → Row 4
J-4k = 0
M-5k = 0
Z-3k = 0
-M+Z+4k = 16

Row 4 + Row 2 → Row 4
J-4k = 0
M-5k = 0
Z-3k = 0
Z-k = 16

Row 4 - Row 3 → Row 4
J-4k = 0
M-5k = 0
Z-3k = 0
2k = 16


k = 16/2 = 8
Z = 0+3k = 0+3 · 8 = 24
M = 0+5k = 0+5 · 8 = 40
J = 0+4k = 0+4 · 8 = 32

J = 32
M = 40
Z = 24
k = 8

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