Question

Mai is filling her fish tank. Water flows into the tank at a constant rate. Complete the table as you answer the questions.
A. How many gallons of water will be in the fish tank after 3 minutes? Explain your reasoning.
B. How long will it take to fill the tank with 40 gallons of water? Explain your reasoning.
C. What is the constant of proportionality?
time (minutes) water (gallons)
row 1 0.5 0.8
row 2 1 row 3 3 row 4 40

Answer 1

Step-by-step explanation:

Answer :

The original fraction is $\sf \dfrac{23}{27}$

Step by Step Explanation :

Let for the original fraction ;

Numerator be = x

As per the given condition - Denominator of the fraction is greater than and it's numerator by 4 therefore,

Denominator must be = x + 4

By Numerator and Denominator ,

Original Fraction is : $\rm\dfrac{x}{x+ 7}$

$\large \bigstar$ When the numerator is increased by 7 and denominator is decreased by 2 ;

Fraction becomes : $\rm \dfrac{(x) + 7}{(x + 4) - 2}$

Therefore,

New Fraction is : $\rm\dfrac{x + 7}{x + 2}$

$\large \dashrightarrow$ According To Question ;

$\Large \dag \large \: \: \: \underline{ \boxed{ \bf \frac{x + 7}{x + 2} = \frac{6}{5} }}$

➡️ On cross multiplication :

$\\ :\longmapsto \rm 5(x + 7) = 6(x + 2)$

$:\longmapsto \rm 5x + 35 = 6x + 12$

$:\longmapsto \rm 5x - 6x = 12 - 35$

$:\longmapsto \rm \cancel - x = \cancel - 23$

$\red{:\longmapsto \bf \underbrace{\underline{ \blue{x = 23 }}}}$

As we assumed numerator as x so,

Numerator of original fraction = 23

As per the question denominator of the fraction is greater than and it's numerator by 4

$\therefore \:$ Denominator = 23 + 4

Hence,

Denominator of original fraction = 27

Therefore,

Original Fraction is : $\sf \dfrac{23}{27}$