Question

A landscaper needs 3 4/8 pounds of plant food. He has 1 1/4 pounds in his truck, and another 4/6 pound at his shop. How many more pounds of plant food does the landscaper need? Enter your answer as a mixed number in simplest form as a fracren plz help

Answer 1

`(19)/(12)\ pounds`

or

`1(7)/(12)\ pounds`

Explanation:

Let

x ----> the additional pounds of plant food needed for the landscaper

we know that

The additional pounds of plant food needed for the landscaper plus the pounds in his truck plus the pounds in his shop must be equal to the total pounds of plant food needed

so

The linear equation that represent this problem is

`x+1(1)/(4)+(4)/(6)=3(4)/(8)`

Convert mixed number to an improper fractions

`1(1)/(4)=1+(1)/(4)=(4*1+1)/(4)=(5)/(4)`

`3(4)/(8)=3+(4)/(8)=(3*8+4)/(8)=(28)/(8)=(14)/(4)`

Substitute in the expression above

`x+(5)/(4)+(4)/(6)=(14)/(4)`

solve for x

Multiply by (4*6) both sides to remove the fractions

`24x+30+16=84`

Combine like terms left side

`24x+46=84`

subtract 46 both sides

`24x=84-46`

`24x=38`

Divide by 24 both sides

`x=(38)/(24)\ pounds`

simplify

`x=(19)/(12)\ pounds`

Convert to mixed number

`(19)/(12)\ pounds=(12)/(12)+(7)/(12)=1(7)/(12)\ pounds`