jessie had 7 pets she had horses ducks and spiders altogether they had 30 legs. how many of each pet did she own
ducks 3 horses 2 spiders 2
Correct
Well, let's do the math and solve this leggy puzzle.
First, let's assign variables to represent the number of each pet. Let's call the number of horses H, the number of ducks D, and the number of spiders S.
Horses have 4 legs each, so Jessie's horses would contribute 4H legs.
Ducks have 2 legs each, so Jessie's ducks would contribute 2D legs.
And spiders have 8 legs each, so Jessie's spiders would contribute 8S legs.
We know that Jessie's pets altogether had 30 legs, so we can write an equation:
4H + 2D + 8S = 30.
Now let's use our detective skills to solve this. But before we begin, let me juggle some circus balls to get my clown brain working at its full capacity.
*clown juggles balls*
Alright, let's simplify the equation a bit. Divide everything by 2, so we get:
2H + D + 4S = 15.
Hmm, this equation doesn't give us a single answer. But fear not, my friend, there are multiple solutions that satisfy this equation. So let's explore a few possibilities:
1. If Jessie has 2 horses (H = 2), 5 ducks (D = 5), and no spiders (S = 0), the equation holds true: 2(2) + 5 + 4(0) = 4 + 5 + 0 = 9.
2. If Jessie has 4 horses (H = 4), 1 duck (D = 1), and 2 spiders (S = 2), the equation also holds true: 2(4) + 1 + 4(2) = 8 + 1 + 8 = 17.
3. If Jessie has 1 horse (H = 1), 10 ducks (D = 10), and 1 spider (S = 1), the equation still holds true: 2(1) + 10 + 4(1) = 2 + 10 + 4 = 16.
So, my dear friend, there could be multiple combinations of pets that add up to 30 legs. Jessie could have 2 horses and 5 ducks, or 4 horses and 1 duck, or even 1 horse and 10 ducks. As for the spiders, they seem pretty shy and may not be part of the scenario. Always remember, the world of possibilities is full of laughter and surprises!
Let's solve this problem step by step:
Step 1: Assign variables.
Let's assume:
H = number of horses
D = number of ducks
S = number of spiders
Step 2: Determine the number of legs each type of pet has.
Horses have 4 legs.
Ducks have 2 legs.
Spiders have 8 legs.
Step 3: Write equations.
From the problem, we know:
H + D + S = 7 (since Jessie had a total of 7 pets)
4H + 2D + 8S = 30 (since the total number of legs equals 30)
Step 4: Solve the equations.
We can solve the equations using any suitable method. In this case, we'll solve them using substitution or elimination.
Using substitution:
From the first equation, we can express H in terms of D and S:
H = 7 - D - S
Substituting this expression into the second equation, we get:
4(7 - D - S) + 2D + 8S = 30
28 - 4D - 4S + 2D + 8S = 30
-2D + 4S = 2
-2(D - 2S) = 2
D - 2S = -1 -- (Equation 3)
Now, we have two equations:
D - 2S = -1 -- (Equation 3)
H + D + S = 7 -- (Equation 1)
Let's solve Equation 3 for D:
D = 2S - 1
Now, substitute D in Equation 1:
H + (2S - 1) + S = 7
H + 3S - 1 = 7
H + 3S = 8 -- (Equation 4)
Step 5: Find the values of H, D, and S.
To solve for H, D, and S, we need to find a combination of values that satisfy both Equation 3 and Equation 4.
Let's try different values of S:
When S = 1:
H + 3(1) = 8
H = 5
When S = 2:
H + 3(2) = 8
H = 2
When S = 3:
H + 3(3) = 8
H = -1
Since we cannot have a negative number of pets, we can conclude that the values S = 2, H = 2, and D = 3 satisfy both equations.
Therefore, Jessie had 2 horses, 3 ducks, and 2 spiders.
To find out how many of each pet Jessie owned, we can use a system of equations.
Let's assign variables to each type of pet:
- H: number of horses
- D: number of ducks
- S: number of spiders
We know that horses have 4 legs, ducks have 2 legs, and spiders have 8 legs. We also know that there are a total of 30 legs.
So we can write two equations based on the given information:
1. The total number of pets: H + D + S = 7
2. The total number of legs: 4H + 2D + 8S = 30
Now we have a system of two equations with two unknowns. We can solve it using substitution or elimination.
Let's solve it by substitution:
From equation 1, we can express H in terms of D and S:
H = 7 - D - S
Substitute this value of H into equation 2:
4(7 - D - S) + 2D + 8S = 30
28 - 4D - 4S + 2D + 8S = 30
28 - 2D + 4S = 30
-2D + 4S = 2
-2D = -4S + 2
2D = 4S - 2
D = (4S - 2)/2
D = 2S - 1
Now we can substitute this expression for D into equation 1:
(2S - 1) + D + S = 7
3S = 8
S = 8/3
Since the number of pets cannot be fractional, we can disregard the solution with fractional values for S.
Therefore, there are multiple possible solutions depending on the value of S. For whole numbers of pets, we need to find values of S, D, and H that satisfy the conditions:
- Let's take S = 1 (1 spider).
- Substituting S = 1 into the equation D = 2S - 1:
D = 2(1) - 1 = 2 - 1 = 1.
- Calculating the remaining pet, H = 7 - D - S:
H = 7 - 1 - 1 = 5.
Therefore, Jessie owns 5 horses, 1 duck, and 1 spider.