Can you help me solve this?

Question

A landscaper buys 4 peonies and 9 geraniums for $190. Another buys 5 peonies and 6 geraniums for $185. Find the cost for one peony and one geranium. 

Answer 1

Here,

 

Let Peonies be X and Geraniums be Y

 

So, as per the question

 

4X+ 9Y = 190     eq-1

5X+ 6Y = 185     eq-2

 

Solving eq 1 and eq 2

 

Multiplying eq 1 by 2 and eq 2 by 3

 

4X+ 9Y = 190 * 2

5X+ 6Y = 185 * 3

 

we get

 8X + 18Y = 380

15X + 18Y = 555

 

(Changing the signs of positive in to negative in eq 2 ) we get

 

-7X= -175

X= -175/-7

X= 25

 

Putting the value of X in eq 1

 

4X+ 9Y = 190

4*25 + 9Y = 190

9Y=190-100

Y= 90/9

Y=10

 

Therefore, cost of 1 peonies  is $25 and 1  geraniums is $10.

Answer 2

4p+9g=190

5p+6g=185

multiply the top equation by -5 and the bottom equation by 4 (there are other ways to do this also)

-20p-45g=-950

20p+24g=740

add

-21g=-210

-210/-21=g

g=10 geraniums

4p+9(10)=190

4p+90=190

4p=190-90

4p=100

p=100/4

p=25 peonies