There are 24 students in a seventh grade class. they decided to plant birches and roses at the school's backyard. while each girl planted 3 roses, every three boys planted 1 birch. by the end of the day they planted 24 plants. how many birches and roses were planted?

Let the number of boys be x. Let the number of girls be y.

Since there are 24 students that means:          x + y = 24(a)

Since each girl planted 3 roses, so they must have planted  3*y = 3y  roses

Since every 3 boys planted 1 birch, so they must have planted x÷3 = x/3 birches

Since total number of plants = 24

Therefore:          x/3  + 3y = 24(b)                  Multiply through by 3
                          x  + 9y = 72  (c)

x + y = 24(a)
-
x  + 9y = 72  (c)


Equation (a) minus (c)

0x - 8y   =  -48
-8y     =   - 48
y     = -48/8
y = 6

Substitute into:   x  + y = 24  (a) 

x + 6 = 24
x  =   24 - 6
x  = 18

Therefore number of boys x is 18 and number of girls y is 6.

Number of plants is from equation (c)  x/3,   and 3y  =

x/3 = 18/3 = 6
3y = 3*6 = 18

6 birches and 18 roses were planted.      

I hope this helps.