An ant has 6 legs and a Spider has 8 legs. In a insectarium display, there are some spiders and ants. From these spiders and ants, there are 60 legs altogether. how many spiders and ants could there be?
A = 6/8S
6A + 8S = 60
Substitute 6/8S for A in second equation and solve for S. Then use first equation to find A.
To solve this problem, let's assume that the number of ants is represented by 'A' and the number of spiders is represented by 'S'.
Since an ant has 6 legs and a spider has 8 legs, we can create two equations representing the total number of legs from ants and spiders:
Number of ant legs: 6A
Number of spider legs: 8S
It is also given that the total number of legs from ants and spiders is 60:
6A + 8S = 60
Now we can use this equation to find the possible combinations of ants and spiders that satisfy the condition.
To simplify the equation, we can divide both sides by 2:
3A + 4S = 30
We can proceed further by assigning arbitrary values to either A or S and then solving for the other variable.
Let's assume the number of ants (A) is 0. This means we only have spiders, and the equation becomes:
4S = 30
S = 7.5
Since the number of spiders must be a whole number, we know that assuming A is 0 is not possible.
Let's try another assumption by setting the number of spiders (S) to 0. This means we only have ants, and the equation becomes:
3A = 30
A = 10
This assumption works since both A and S are whole numbers. So, if there are 10 ants, the total number of legs would be:
6 * 10 = 60
However, we should also try to find if there are any other combinations that satisfy the equation. To do this, we can increment the number of spiders (S) by 1 and solve for the number of ants (A).
Let's assume S is 1:
3A + 4 * 1 = 30
3A = 26
A ≈ 8.67
Since A is not a whole number, this assumption does not work.
From our analysis, the possible combination is 10 ants and 0 spiders. Therefore, there could be 10 ants and no spiders in the insectarium display.