The number of monkeys in a cage is 8 more
than the number of birds in the cage. There
are 22 animals in the cage. Find the number
of monkeys in the cage.
To solve the problem, we have two pieces of information which we can use to form equations.
1. The number of monkeys is 8 more than the number of birds.
2. There are a total of 22 animals in the cage.
Let's assign variables to represent the number of birds and monkeys:
Let the number of birds be \(x\).
According to the first piece of information, the number of monkeys will then be \(x + 8\).
Using the second piece of information about the total number of animals, we can write an equation that represents the sum of the birds and monkeys:
\(x\) (birds) + \(x + 8\) (monkeys) = 22 (total animals)
Combining like terms in this equation gives us:
\(2x + 8 = 22\)
To find the value of \(x\), we first isolate the variable term (2x) by subtracting 8 from both sides of the equation:
\(2x = 22 - 8\)
\(2x = 14\)
Now we divide both sides by 2 to solve for \(x\):
\(x = \frac{14}{2}\)
\(x = 7\)
Now that we have the number of birds, which is 7, we can find the number of monkeys by remembering that there are 8 more monkeys than birds:
Number of monkeys = Number of birds + 8
Number of monkeys = 7 + 8
Therefore, the number of monkeys is 15.
