Question

Mark wants to paint a mural. He has 1 1/5 gallons of yellow paint, 1 1/6 gallons of green paint, and 7/8 gallon of blue paint. Mark plans to use 3/4 gallon of each paint color. How many gallons of paint will he have left after painting the mural? Enter your answer as a simplified fraction.

Answer 1

`(119)/(120)\ gal`

Explanation:

we know that

The algebraic expression to find out how many gallons of paint he will have left after painting the mural is equal to

`(1(1)/(5)-(3)/(4)) + (1(1)/(6)-(3)/(4))+((7)/(8)-(3)/(4))`

Convert mixed numbers to an improper fractions

`1(1)/(5)=1+(1)/(5)=(1*5+1)/(5)=(6)/(5)`

`1(1)/(6)=1+(1)/(6)=(1*6+1)/(6)=(7)/(6)`

substitute

`((6)/(5)-(3)/(4)) + ((7)/(6)-(3)/(4))+((7)/(8)-(3)/(4))`

Find the least common multiple (LCM) for the denominators

`((4*6-3*5)/(20)) + ((2*7-3*3)/(12))+((7-3*2)/(8))`

`((9)/(20)) + ((5)/(12))+((1)/(8))`

Find the least common multiple (LCM) for the denominators

The LCD is

`(2^3)(3)(5)=120`

`((9*6+5*10+1*15)/(120))`

`(119)/(120)\ gal`