A spider has 8 legs, a dragonfly has 6 legs. Given a number of spiders and
dragonflies altogether have 420 legs, number of spiders are 3 times the
number of dragonflies, the number of spiders are?
8s+6d=420
3D= s
8s+6(s/3)=420
10s=420
s= 42
Let's use variables to represent the unknowns in the problem.
Let's say the number of spiders is S and the number of dragonflies is D.
Given that a spider has 8 legs and a dragonfly has 6 legs, we can write an equation for the total number of legs:
8S + 6D = 420 (Equation 1)
Given that the number of spiders is 3 times the number of dragonflies, we can write another equation:
S = 3D (Equation 2)
Now we can solve this system of equations to find the values of S and D.
Substitute the value of S from Equation 2 into Equation 1:
8(3D) + 6D = 420
24D + 6D = 420
30D = 420
Divide both sides of the equation by 30:
D = 420/30
D = 14
Now substitute the value of D into Equation 2 to find S:
S = 3(14)
S = 42
So, the number of spiders is 42.
To find the number of spiders, we can set up an equation using the given information.
Let's denote the number of spiders as "x" and the number of dragonflies as "y".
According to the given information:
- A spider has 8 legs, so the total number of spider legs would be 8 times the number of spiders: 8x.
- A dragonfly has 6 legs, so the total number of dragonfly legs would be 6 times the number of dragonflies: 6y.
We are also given that the total number of legs from spiders and dragonflies combined is 420 legs. So, we can set up the equation:
8x + 6y = 420
Additionally, the number of spiders is mentioned to be 3 times the number of dragonflies:
x = 3y
Now that we have two equations, we can solve them simultaneously to find the values of x and y.
Using the second equation, we can substitute x in terms of y into the first equation:
8(3y) + 6y = 420
24y + 6y = 420
30y = 420
y = 420 / 30
y = 14
Now, we can substitute the value of y back into the second equation to find x:
x = 3y
x = 3 * 14
x = 42
Therefore, the number of spiders is 42.