how many gallons can it hold

Question

The container that holds the water for the football team is
7/10
full. After pouring out
6
gallons of water, it is
1/2
full. How many gallons can the container hold?

Answer 1

Re-phrasing:   "7/10 full minus 6 gallons is 1/2 full"

 

Let x= the number of gallons when full

 

"7/10 full minus 6 gallons is 1/2 full"    means

  (7/10)x - 6 = (1/2)x

 

 (7/10)x - (1/2)x = 6      [subtract (1/2)x from both sides; add 6 to both sides]

  (7/10)x - (5/10)x = 6      [make common denominator so we can subtract]

    (2/10)x = 6

     x = 6(10/2)                  [multiply both sides by (10/2)

    x = 30 gallons

 

Checking (very important):

  Is  (7/10)(30) - 6 = (1/2)(30)   ?

        21 - 6 = 15    ?yes

Answer 2

Alyssa,

 

6 gallons of water represents 7/10 - 1/2 of the container

 

7/10 - 1/2 = 7/10-5/10 = 2/10 or 1/5

 

6 gallons is 1/5 of the container

 

The container holds 30 gallons (6 x 5)

 

If you can't see this immediately, set up a proportion

 

6        1

--  =  --

x       5

 

and cross multiple.