Question

In a finsh tank, 75% is female finshes. The rest are male. Female fishes are also 5 more than twice
of the male fishes. How many female and male fishes in the tank?
(Set up the rational equation, and solve for x!) PLEASE HELP ME

Answer 1

Answer:

5 Male fishes, and 15 Female fishes

Step-by-step explanation:

We have two unknowns: The number of lady fishes (let's represent this number with "L"), and the number of male fishes (let's name this unknown number "M"). So now we need to create two equations to help us solve for these unknowns.

Use the actual sentences they give you to create the equations:

a) "75% of the total number of fishes are female"

Notice that the total number of fishes is the addition of the number of ladies plus the number of males; that is the total is "L+M". According to the sentence, 75% (which in math terms is written as "0.75") of this total number equals the number of lady fishes:

$0.75 \,*\,(L+M)=L$

now we work a little the algebra indicated in this equation to simplify it a bit:

$0.75 \,*\,(L+M)=L\\0.75\,L+0.75\,M=L\\0.75\,M=L-0.75\,L\\0.75\,M=0.25\,L\\L=\frac{ 0.75\,M}{0.25}\\L=3\,M$

which tells us that the number of lady fishes is 3 times thenumber of male fishes.

b) Now the second equation based on the words:

"Lady fishes are 5 more than twice the male fishes"

"Twice the male fishes" can be written as: "2M"

so now we write this sentence as:

$L=2\,M+5$

Now we combine the two equations by using in the second one the replacement for "L" in terms of "M" that we found in the first equation (that is: "L = 3 M") , so we obtain an equation with just one unknown (M) and we can solve for it:

$L=2\,M+5\\3\,M=2\,M+5\\3\,M-2\,M=5\\M=5$

Which tells us that the number of male fishes in the tank is "5".

We can use now our first simplified equation to find the number of lady fishes:

$L=3\,M\\L=3\,(5)\\L=15$

So, there are 15 female fishes in the tank.