Solving the Chickens and Goats Riddle
This problem involves setting up and solving a system of linear equations based on the given information about heads and legs.
Setting Up the Equations
Let $C$ represent the number of chickens and $G$ represent the number of goats.
- Heads Equation: Each animal has one head. $ C + G = 42 $
- Legs Equation: Chickens have 2 legs and goats have 4 legs. $ 2C + 4G = 138 $
Solving for the Number of Chickens ($C$)
We can use the substitution method. First, express $G$ in terms of $C$ using the heads equation:
From $C + G = 42$, we get $G = 42 - C$.
Now, substitute this expression for $G$ into the legs equation:
$ 2C + 4(42 - C) = 138 $Simplify and solve for $C$:
- Distribute the 4: $2C + 168 - 4C = 138$
- Combine the $C$ terms: $168 - 2C = 138$
- Subtract 168 from both sides: $-2C = 138 - 168$
- Calculate the difference: $-2C = -30$
- Divide by -2: $C = \frac{-30}{-2}$
- Result: $C = 15$
Therefore, there are 15 chickens.
Verification (Optional)
If $C = 15$, then $G = 42 - 15 = 27$.
Check the total legs: $(2 \times 15) + (4 \times 27) = 30 + 108 = 138$. The calculation is correct.
Similar Questions
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Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
