A herd consists of camels and dromedaries. There are 180 heads and 304 bumps. How many dromedaries are there if camels have two humps each and dromedaries have one hump each?

Step 1: Define variables

We first define variables to represent the unknown quantities in the problem. Let $c$ be the number of camels and $d$ be the number of dromedaries.

Step 2: Formulate equation based on heads

Each animal has one head. Since there are a total of 180 heads, the sum of the number of camels and dromedaries must be 180. This gives us our first linear equation.

Step 3: Formulate equation based on humps

Each camel has two humps, and each dromedary has one hump. The total number of humps is 304. So, two times the number of camels plus one times the number of dromedaries equals 304. This forms our second linear equation.

Step 4: Solve the system of equations

We can use the substitution method to solve the system of linear equations. From the first equation, we express $c$ in terms of $d$. Then we substitute this expression for $c$ into the second equation.

Step 5: Simplify and solve for d

Now we simplify the equation obtained in the previous step. We combine the terms involving $d$ and then isolate $d$ to find its value. Performing the subtraction, we find $d$ to be 56.

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