a gas tank is 3/8 full. When 3 gallons are added, the tank is 9/16 full. How many gallons does a full tank hold?

Question

4th grade word problem.

Answer 1

Hi Nancy,

 

How to set it up?

 

You have (3/8) T and you add 3 gallons and you get (9/16) T: T = Tank.

 

So, write as: (3/8)T + 3 = (9/16)T.  LCD (Least Common Denominator) is 16 for 8 & 16.

 

So, rewrite as (6/16)T + 3 = (9/16)T.  Now, you subtract (6/16)T from both sides and you will be left with:

3 = (3/16)T.  As you divide 3 into (3/16)T, you should get 16 for T.  And this Tank holds 16 gallons.

 

Let's check it:  put 16 for T to original problem.  (3/8) * 16 + 3 = (9/16) * 16

(3/8) * 16 = 6 and (9/16) * 16 = 9.  So, 6+3 = 9.  And it does checks out.

 

So, it means that this Tank had 6-gallons (3/8) and has added 3-gallons to achieve 9-gallons (9/16) out of 16-gallon (full tank capacity).

 

Good luck to you.