Question

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?

Answer 1

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)
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x + 9y = 72 .....(c)
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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.