Question

Flies cannot see much farther than 24 to 36 inches away for their eyes, but that is not due to a lack of lenses-dragonflies have thousands of lenses! In one eye, dragonflies have 2000 more lenses than seven times the number of lenses that houseflies have in one eye if one housefly and one dragonfly eye together have 34000 lenses, how many lenses do houseflies have in one eye? How many do dragonflies have in one eye

Answer 1

Answer:

The number of lenses in one eye of the dragonfly is 30,000

Step-by-step explanation:

Before we calculate the quantity of lenses in one eye of the dragonfly, let us denote the number of lenses in one eye of the dragonfly by "x" and denote the quantity of lenses in one eye of the housefly by "y".

Now, since dragonflies in one eye have 2,000 more lenses than seven times the number that houseflies have, we can represent this mathematically:-

x = 2000 + [7×(y)]

x = 2000 + 7y

Again we learnt that the number of lenses in one eye of the dragonfly plus the number of lenses in the housefly are equal to thirty - four thousand lenses. mathematically:-

x + y = 34000

We now have a set of two equations which are:

2000 + 7y = x ------------ 1

x + y = 34000 ----------- 2

The resulting simultaneous equation can then be solved using elimination or substitution method. Let us use substitution method to solve solve for "y".

In equation 1, x = 2000 + 7y.

We can substitute "x" for 2000 + 7y in equation 2

2000 + 7y + y = 34,000

2000 + 8y = 34,000

8y = 34,000 - 2,000

8y = 32,000

y = 32000/8

y = 4,000 lenses. This is the number of lenses in one eye of the housefly.

Now, substitute y for 4,000 in equation 1 in order to find "x".

x = 2000 + 7(4000)

x = 2000 + 28000

x = 30000 lenses.

Therefore the number of lenses in one eye of the dragonfly is 30,000 lenses.