Question

i had 3 times as many rose bushes as holly bushes in my garden. Then i moved seven of my rose bushes to my grandfather’s garden, and i planted 11 new holly bushes in my garden. Now my garden gas half as many rose bushes as holly bushes. How many rose bushes and holly bushes, in all, did i have initially

Answer 1

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

Learn more on system of linear equations here: brainly.com/question/13729904