Question

At the zoo tje ratio of snakes to lizards is 3:2 A. If there were 10 lizards ,how many snakes would be there be? B.If there were 9 snakes ,how many lizards would there be? C.If the number of snakes in the zoo is increased by 6, how many more lizards would the zoo need to get to keep the same ratio? D. If the total number of snakes ang lizards at the zoo was 20, how many snakes and lizards would there be? WITH CALCULATION AND STEPS PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Answer 1

Snake and Lizard Ratios at the Zoo:

A. If there were 10 lizards:

Since the ratio of snakes to lizards is 3:2, for every 2 lizards, there are 3 snakes.

Therefore, if there are 10 lizards, we have 10 lizards * (3 snakes / 2 lizards) = 15 snakes at the zoo.

B. If there were 9 snakes:

Working backwards, we can find the corresponding number of lizards using the same ratio.

Divide the number of snakes by 3 and multiply by 2: 9 snakes / 3 = 3 lizards * 2 = 6 lizards.

C. If the number of snakes is increased by 6:

First, find the original number of snakes: 15 snakes (from part A) - 6 additional snakes = 9 snakes.

To maintain the 3:2 ratio, we need to increase the number of lizards by the same proportion as the increase in snakes.

Increase the number of lizards by 6 lizards * (2 lizards / 3 snakes) = 4 more lizards.

D. If the total number of snakes and lizards was 20:

Let x be the number of snakes and y be the number of lizards.

We know the total number is 20: x + y = 20.

We also know the ratio of snakes to lizards is 3:2, which can be written as x/y = 3/2.

Solve the system of equations:

From the first equation, y = 20 - x.

Substitute this into the second equation: x / (20 - x) = 3/2.

Solve for x: x ≈ 12.

Therefore,

Answer 2

Part A)
`15\ snakes`

Part B)
`6\ lizards`

Part C) The zoo would need to get four more lizards to maintain the same proportion

Part D) 12 snakes and 8 lizards

Explanation:

Part A) If there were 10 lizards ,how many snakes would be there be?

Let

x ---> the number of snakes

y ---> the number of lizards

`(x)/(y)=(3)/(2)` ----> equation A

we have that

`y=10\ lizards`

substitute the value of y in the equation A

`(x)/(10)=(3)/(2)`

solve for x

`x=10(3)/2\\x=15\ snakes`

Part B) If there were 9 snakes ,how many lizards would there be?

Let

x ---> the number of snakes

y ---> the number of lizards

`(x)/(y)=(3)/(2)` ----> equation A

we have that

`x=9\ snakes`

substitute the value of x in the equation A

`(9)/(y)=(3)/(2)`

solve for y

`y=9(2)/3\\y=6\ lizards`

Part C) If the number of snakes in the zoo is increased by 6, how many more lizards would the zoo need to get to keep the same ratio?

Let

x ---> the number of snakes

y ---> the number of lizards

`(x)/(y)=(3)/(2)` ----> equation A

For
`x=6\ snakes`

substitute the value of x in the equation A

`(6)/(y)=(3)/(2)`

solve for y

`y=6(2)/3\\y=4\ lizards`

therefore

The zoo would need to get four more lizards to maintain the same proportion

Part D) If the total number of snakes and lizards at the zoo was 20, how many snakes and lizards would there be?

Let

x ---> the number of snakes

y ---> the number of lizards

`(x)/(y)=(3)/(2)`

isolate the variable x

`x=1.5y` ----> equation A

`x+y=20` ----> equation B

solve the system by substitution

substitute equation A in equation B

`1.5y+y=20`

solve for y

`2.5y=20`

`y=8\ lizards`

Find the value of x

`x=1.5(8)=12\ snakes`

therefore

12 snakes and 8 lizards