Canapés on plates

On the table there were 18 plates. On each plate there was the same number of canapés. Tomáš with his friends took away a third of all the plates with canapés. Lenka for her friends took from each of the remaining plates 3 canapés. On the table there thus remained half of the original number of canapés. How many canapés did Lenka take for her friends? How many canapés remained on the table? How many canapés did Tomáš and his friends take away?

Final Answer:

j =  216
l =  36
t =  72
x =  12

Step-by-step explanation:


18x = j
j - t - l = j/2
t = 18/3 · x
l = 3·(18 - 18/3)

18·x = j
j - t - l = j/2
t = 18/3 · x
l = 3·(18 - 18/3)

j-18x = 0
j-2l-2t = 0
3t-18x = 0
3l = 108

Row 2 - Row 1 → Row 2
j-18x = 0
-2l-2t+18x = 0
3t-18x = 0
3l = 108

Pivot: Row 2 ↔ Row 4
j-18x = 0
3l = 108
3t-18x = 0
-2l-2t+18x = 0

Row 4 - -2/3 · Row 2 → Row 4
j-18x = 0
3l = 108
3t-18x = 0
-2t+18x = 72

Row 4 - -2/3 · Row 3 → Row 4
j-18x = 0
3l = 108
3t-18x = 0
6x = 72


x = 72/6 = 12
t = 0+18x/3 = 0+18 · 12/3 = 72
l = 108/3 = 36
j = 0+18x = 0+18 · 12 = 216

j = 216
l = 36
t = 72
x = 12

Our linear equations calculator calculates it.



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