Seedlings in a garden centre

In three garden centres they grow roses, pansies, and narcissi. Find out their numbers.
a) In the blue garden centre they have in total 200 seedlings. Of these, half are pansies, and pansies with narcissi together make 150.
roses:
narcissi:
pansies:

b) In the yellow garden centre they have in total 130 seedlings. Pansies and roses together make 115. Roses are 60 more than narcissi.
pansies:
roses:
narcissi:

c) In the green garden centre they have in total 139 pieces of seedlings. Pansies and narcissi together make 55 pieces. Roses are 4 times more than narcissi.
pansies:
roses:
narcissi:

Final Answer:

m = 100
n = 50
r = 50
m₂ = 40
n₂ = 15
r₂ = 75
m₃ = 34
n₃ = 21
r₃ = 84

Step-by-step explanation:

r+n+m=200
m = 200/2
m+n=150

m+n+r = 200
2m = 200
m+n = 150

Pivot: Row 1 ↔ Row 2
2m = 200
m+n+r = 200
m+n = 150

Row 2 - 1/2 · Row 1 → Row 2
2m = 200
n+r = 100
m+n = 150

Row 3 - 1/2 · Row 1 → Row 3
2m = 200
n+r = 100
n = 50

Row 3 - Row 2 → Row 3
2m = 200
n+r = 100
-r = -50

r = -50/-1 = 50
n = 100-r = 100-50 = 50
m = 200/2 = 100

m = 100
n = 50
r = 50

Our linear equations calculator calculates it.

m₂+r₂+n₂=130
m₂+r₂=115
r₂=60+n₂

m₂+n₂+r₂ = 130
m₂+r₂ = 115
n₂-r₂ = -60

Row 2 - Row 1 → Row 2
m₂+n₂+r₂ = 130
-n₂ = -15
n₂-r₂ = -60

Row 3 + Row 2 → Row 3
m₂+n₂+r₂ = 130
-n₂ = -15
-r₂ = -75

r2 = -75/-1 = 75
n2 = -15/-1 = 15
m2 = 130-n2-r2 = 130-15-75 = 40

m₂ = 40
n₂ = 15
r₂ = 75

Our linear equations calculator calculates it.

m₃+n₃=55
r₃=4·n₃
m₃+r₃+n₃=139

m₃+n₃ = 55
4n₃-r₃ = 0
m₃+n₃+r₃ = 139

Row 3 - Row 1 → Row 3
m₃+n₃ = 55
4n₃-r₃ = 0
r₃ = 84

r3 = 84/1 = 84
n3 = 0+r3/4 = 0+84/4 = 21
m3 = 55-n3 = 55-21 = 34

m₃ = 34
n₃ = 21
r₃ = 84

Our linear equations calculator calculates it.