Question

Amy and rob each improve thier yards by pmanting rose bushes and ivy. They brought thier supplies from the same store. Amy spent 82 dollars on 7 rose bushes and 1 pot of ivy. Rob spend 74 on 5 rose bushes and 2 pots of ivy. Find the cost of the one rose bush and one pot of ivy

Answer 1

Answer: cost of 1 pot of ivy = $12

Cost of 1 rose bush =$ 10

Step-by-step explanation:

Step 1

Let rose bushes be represented as r

and pot of ivy be represented as p

such that Amy who spent 82 dollars on 7 rose bushes and 1 pot of ivy can be expressed as

7 r + p = 82----- eqn 1

Rob who spent 74 on 5 rose bushes and 2 pots of ivy can  be expressed as

5r +2 p = 74----- eqn 2

Step 2

Solving

7 r + p = 82----- eqn 1

5r +2 p = 74----- eqn 2

By elimination method Multiply eqn 1 by 5 and eqn 2 by 7

35r+ 5p= 410--- eqn 3

35r+ 14p =518--- eqn 4

Subtracting eqn 4 from eqn 3

9p = 108

p = 108/9

p=12

p = pot of ivy = $12

therefore rose bush  wll be ( from equation 1)

7r+ p= 82

7r=82-12

7r= 70 r= 70/7

r= rose bush =$ 10