there ae 46 legs in a zoo exihibit. every animal has either 2 or 4 legs. the expression 2m+4n is the total number of legs for m 2 legged animals and n 4 legged animals in the exihibit

a. list possible values for m and n so that the total number of legs is 46

b. The number of 2 legged animas is 2 more than the number of 4 legged animals. how many of each are in the exhibit?

c. The number of legs in the exhibit increases by 4. what might account for this increase?

a. Possible values for m and n to achieve a total number of 46 legs are: m = 23 and n = 11; m = 22 and n = 12; m = 21 and n = 13; m = 20 and n = 14; m = 19 and n = 15; m = 18 and n = 16.

b. If the number of 2 legged animals is 2 more than the number of 4 legged animals, there must be 24 2 legged animals and 22 4 legged animals in the exhibit (24 + 22 = 46).

c. The increase in the number of legs in the exhibit might be due to the addition of a new animal to the exhibit. If the new animal has 4 legs, the total number of legs in the exhibit will increase by 4.

semsee45 semsee45 · Answer 2 · 2023-01-14T23:45:00+01:00

Answer:

a) Possible values of m and n:

m = 23, n = 0
m = 21, n = 1
m = 19, n = 2
m = 17, n = 3
m = 15, n = 4
m = 13, n = 5
m = 11, n = 6
m = 9, n = 7
m = 7, n = 8
m = 5, n = 9
m = 3, n = 10
m = 1, n = 11

b) 9 two-legged animals and 7 four-legged animals.

c) Either 1 four-legged animal or 2 two-legged animals have been added to the exhibit.

Step-by-step explanation:

Given expression:

2m + 4n = 46

where:

m = 2 legged animals
n = 4 legged animals

Part a

Calculate the greatest number of four-legged animals by dividing the total number of animals by 4:

[tex]\implies 46 \div 4 = 11.5[/tex]

Therefore, the greatest number of four-legged animals is 11.

When there are no four-legged animals, n = 0.

Substitute n = 0 into the given equation:

[tex]\begin{aligned}\implies 2m+4(0)&=46\\2m&=46\\ m&=23\end{aligned}[/tex]

Therefore, there are 23 two-legged animals when there are no four-legged animals.

Each time the number of four-legged animals increases by 1, the number of two-legged animals decreases by 2.

Therefore, the possible values for m and n so that the total number of legs is 46 are:

m = 23, n = 0
m = 21, n = 1
m = 19, n = 2
m = 17, n = 3
m = 15, n = 4
m = 13, n = 5
m = 11, n = 6
m = 9, n = 7
m = 7, n = 8
m = 5, n = 9
m = 3, n = 10
m = 1, n = 11

Part b

If the number of two-legged animals is 2 more than the number of four-legged animals then:

m = 9, n = 7

Therefore, there are 9 two-legged animals and 7 four-legged animals.

Part c

If the number of legs in the exhibit increases by 4, then either:

1 four-legged animal has been added to the exhibit, or
2 two-legged animals have been added to the exhibit.