Answer:
8 birds and 6 mice
Step-by-step explanation:
Given:
Number of heads = 14
Number of legs = 40
Required
How many birds and mice are on the ground?
Let M represents Mice and B represents Birds
Birds and Mice have 1 head each;
So;
[tex]B + M = 14[/tex]
Birds have 2 legs; Mice have 4 legs
So;
[tex]2B + 4M = 40[/tex]
At this point, we have two equations;
Make B the subject of formula in the first equation
[tex]B + M = 14[/tex] becomes
[tex]B = 14 - M[/tex]
Substitute 14 - M for B in the second equation
[tex]2(14 - M) + 4M = 40[/tex]
Open bracket
[tex]28 - 2M + 4M = 40[/tex]
[tex]28 + 2M = 40[/tex]
Subtract 28 from both sides
[tex]28 - 28 + 2M = 40 - 28[/tex]
[tex]2M = 40 - 28[/tex]
[tex]2M = 12[/tex]
Divide both sides by 2
[tex]\frac{2M}{2} = \frac{12}{2}[/tex]
[tex]M = 6[/tex]
Recall that [tex]B = 14 - M[/tex]
So;
[tex]B = 14 - 6[/tex]
[tex]B = 8[/tex]
Hence, there are 8 birds and 6 mice
