In a shop, there were 4 times as many guppies as swordtails. After 23 guppies and 27 swordtails were added, there were 83 more guppies than swordtails. What was the total number of fish in the shop at first?

145

Step-by-step explanation:

Assume the number of sword tails is x. Then the number of guppies is 4x.

After 23 guppies and 27 swordtails were added. Then guppies = 4x+ 23

swordtails = x+27

According to the relation 83 more guppies than swordtails. We can obtain:

4x-x= 27+83-23

3x=110-23

3x=87

x=29

There are 5x fish in total at first.

5x=5*29=145

so the number of fish in the shop at first is 145

answer: it is d

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240