Question

Luther's dog eats 5/6 of a can of food each day. Luther currently has 2 1/2 cans of dog food. How many days will the current supply of dog food last?

Answer 1

Answer: The current supply of dog food will last for 3 days.

Explanation:

We are given that:

• Luther's dog eats 5/6 of a can of food each day
• Luther has 2 1/2 cans of dog food

Question:

• How many days will the current supply of dog food last?

First, you need to create a common denominator for the given amounts.

• A common denominator is a number that has at least one factor other than one in common with both denominators.

Values given:

• 5/6
• 2 1/2 -> 5/2

(put 2 1/2 into a improper fraction, so its easier to work with)

The common denominator between 5/6 and 5/2 is 6.

Now convert the fractions into its common denominator.

Since 5/6 already has the denominator of 6, you can leave it as it is.

For 5/2 you convert it like this: 5/2 * 3/3 = 15/6

Next lets go back to the question,

• How many days will the current supply of dog food last?

The question is asking for how many days will the dog food last.

You can find the amount of days it will last by dividing the current amount (total amount of dog food which is 15/6) by the number of food the dog can eat per day (5/6)

• 
  `(15)/(6)`÷
  `(5)/(6)`

That is the same as multiplying 15/6 by the reciprocal of 5/6 (which is 6/5).

• 
  `(15)/(6)`×
  `(6)/(5)`=
  `(90)/(30)`

Then simplify

• 
  `(90)/(30)` = 3

The current supply of dog food will last for 3 days.