Total number of rose and holly bushes that I had initially = 20
System of linear equations
Let the initial number of rose bushes be r
Let the initial number of holly bushes be h
I had 3 times as many rose bushes as holly bushes in my garden
r = 3h......................(1)
After moving seven of my rose bushes to my grandfather’s garden, the remaining number of rose bushes = r - 7
After planting 11 new holly bushes in my garden, the new number of holly bushes = h + 11
Now my garden has half as many rose bushes as holly bushes
r - 7 = 0.5(h + 11)
r = 0.5h + 5.5 + 7
r = 0.5h + 12.5...............(2)
Compare equations (1) and (2)
3h = 0.5h + 12.5
3h - 0.5h = 12.5
2.5h = 12.5
h = 12.5/2.5
h = 5
Substitute h = 5 into equation (1)
r = 3h
r = 3(5)
r = 15
Total number of rose and holly bushes that I had initially = h + r
Total number of rose and holly bushes that I had initially = 5 + 15
Total number of rose and holly bushes that I had initially = 20
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