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 2424 plants. How many birches and roses were planted?
Answers:
A) 6  B) 7  C) 8  D) 2  E) 9

Rationale: let xx be the number of roses . then the number of birches is 24 − x 24 − x , and the number of boys is 3 × ( 24 − x ) 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 x + 216 − 9 x = 72 216 − 72 = 8 x 216 − 72 = 8 x 1448 = x 1448 = x x = 18 x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . answer : a
Answer: A