**A bucket containing 2 2/5 gallons of water is 4/7 full. How many gallons of water is in one fully filled bucket?**

4 1/5

2 1/5

4 4/5

2 2/5

*Correct Answer : A*

we are asked to find the number of gallons a full tank can hold. A full tank is equivalent to 1.

Convert the mixed fraction into proper fraction as follows

(2frac{2}{5}=frac{left(2ast5 ight)+2}{5}=frac{10+2}{5}=frac{12}{5})

If we let x be the number of gallons in full tank, and setting up the proportion equation with the number of gallons on the numerator and fraction of tank on denominator as follows.

(frac{x gallons}{1 full tank}=frac{frac{12}{5} gallons}{frac{4}{7}full tank})

Cross-multiply to find the value of x.

(frac{x }{1 full tank}=frac{frac{12}{5} gallons}{frac{4}{7}full tank})

(x astfrac{4}{7}full tank=frac{12}{5} gallonsast1 full tank)

(x =frac{frac{12}{5} gallonsast1 full tank}{frac{4}{7}full tank}=frac{12}{5}divfrac{4}{7} gallons=frac{12}{5}astfrac{7}{4}gallons=frac{21}{5}gallons)

Converting 21/5 to a mixed fraction is 4 1/5. Thus, when the tank is full, it holds 4 1/5 gallons of water.

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