Can you help with this Algebra 2 word problem

Question

The word problem is: Roses sold for 12 pence each and daffodils sold for 4 pence each. If Jim bought 35 flowers and spent 300 pence, how many daffodils did he buy?

Answer 1

Let D be the number of daffodils and R be the number of roses he bought.

 

The clue of number of flowers bought and amount of money he spent gives two equations.

 

(1)       D +  R =   35

(2)   4D + 12R = 300

 

Divide equation (2) by 4 to get

 

(3)     D + 3R = 75

 

Subtract equation (1) from equation (3) to get

 

(4)     2R = 40

 

Divide by 2

 

R = 20

 

So also D = 35 - 20 = 15

He bought 15 daffodils.

 

Answer 2

You don't know how many roses or how many daffodils there are so there will be two variables

 

r = number of roses

 

d = number of daffodils

 

The total number of flowers is 35 so r + d = 35

 

The total cost is 300 pence so        12r+4d=300

 

Multiply both sides of the top equation by 4 --> 4r + 4d = 140.  Now subtract the other equation so that "d" is no more.

 

                                                                  - (12r +4d = 300)

                                                                 -------------------------

                                                                     -8r = -160

Divide both sides by -8 --> r = 20

 

Plug this number into the first equation and you get d = 15

 

Plug these numbers into the second equation to make sure that it works!