spider and ants after John counted the legs and heads were 68 legs and 10 heads.
a. how many spiders were there?
b. how many ants were there?
heads: s+a=10
legs: 8s+6a=68
Now just solve for s and a.
The picture below shows a group of 10 straws.
How many straws are in 8 of these groups?
A.
8
B.
80
C.
88
D.
800
To determine the number of spiders and ants given the count of legs and heads, we need to use some basic mathematical reasoning.
Let's denote the number of spiders as 's' and the number of ants as 'a'.
Each spider has 8 legs and 1 head, while each ant has 6 legs and 1 head. Therefore, the total number of spider legs can be calculated as 8 times the number of spiders (8s), and the total number of ant legs can be calculated as 6 times the number of ants (6a).
We are given that the total number of legs is 68, so we can translate this information into an equation:
8s + 6a = 68 ---- Equation (1)
Similarly, the total number of heads is given as 10, so we can set up another equation:
s + a = 10 ---- Equation (2)
Now, we have a system of two equations with two unknowns. We can solve this system of equations using various methods, such as substitution or elimination.
Let's solve it using the elimination method. We can multiply Equation (2) by 6 so that the coefficients of 'a' in both equations are equal:
6s + 6a = 60 ---- Equation (3)
Next, we can subtract Equation (3) from Equation (1) to eliminate 'a':
(8s + 6a) - (6s + 6a) = 68 - 60
8s - 6s = 8
2s = 8
s = 4
Now that we have found the value of 's' (the number of spiders), we can substitute it back into Equation (2) to find the value of 'a' (the number of ants):
4 + a = 10
a = 10 - 4
a = 6
So, the solution is:
a. There are 4 spiders.
b. There are 6 ants.