Z7–I–5 MO 2018

At the Rose garden centre, one shop ordered a total of 120 roses in red and yellow, the second shop a total of 105 roses in red and white, and the third shop a total of 45 roses in yellow and white. The garden centre fulfilled the order, in such a way that it delivered the same number of roses of the same colour to each shop.

How many red, how many white and how many yellow roses in total did the garden centre deliver to these three shops?

Final Answer:

b =  30
c =  180
z =  60

Step-by-step explanation:


c/2+z/2 = 120
c/2+b/2 = 105
z/2+b/2 = 45

c+z = 240
b+c = 210
b+z = 90

Pivot: Row 1 ↔ Row 2
b+c = 210
c+z = 240
b+z = 90

Row 3 - Row 1 → Row 3
b+c = 210
c+z = 240
-c+z = -120

Row 3 + Row 2 → Row 3
b+c = 210
c+z = 240
2z = 120


z = 120/2 = 60
c = 240-z = 240-60 = 180
b = 210-c = 210-180 = 30

b = 30
c = 180
z = 60

Our linear equations calculator calculates it.



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