A student has a collection of grasshoppers and crickets. He has 561 insects in all. The number of grasshoppers is twice the number of crickets. Find the number of each type of insects that he has.
Let c = number of crickets
c + 2c = 561
3c = 561
c = 187
To find the number of grasshoppers and crickets, let's assign variables to represent their quantities.
Let's say 'g' represents the number of grasshoppers and 'c' represents the number of crickets.
According to the problem, we know that the student has a total of 561 insects, so we can write the following equation:
g + c = 561
Additionally, we are told that the number of grasshoppers is twice the number of crickets. This can be written as an equation as well:
g = 2c
Now we have a system of equations:
g + c = 561
g = 2c
We can solve this system of equations to find the values of 'g' and 'c'.
Substituting g = 2c into the first equation, we get:
2c + c = 561
3c = 561
c = 561/3
c = 187
Now that we know the value of 'c', we can substitute it back into the equation g = 2c to find 'g':
g = 2(187)
g = 374
Therefore, the student has 374 grasshoppers and 187 crickets.