We are told that our friend's cat weighs 0.83 times the weight of our cat and that our friend's cat weighs 10 pounds. We want to know how much more our cat weighs in comparison. We can do this by rewriting 0.83 as a decimal first.
Writing the Repeating Decimal as a Fraction
The first step to find the weight of our cat is by rewriting the given repeating decimal as a fraction. Let's remember how we can write a repeating decimal as a fraction. We will follow five steps.
We found that x is equal to 7590. Remember that x is also equal to 0.83. The Transitive Property of Equality tells us that the fraction we got is equal to the given repeating decimal number.
x= 0.83 x= 7590 ⇒ 0.83= 75/90
Finding Our Cat's Weight
We found that our friend's cat weighs 7590 times the weight of our cat. From the exercise, we know that our friend's cat weighs 10 pounds. Let's rewrite this as an equation. Let x be the weight of our cat.
75/90 * x = 10
Now let's solve the equation for x to find the weight of our cat.
Our cat weighs 12 pounds. Now, we will find how much more our cat weighs by subtracting the weight of our friend's cat from our cat's weight.
12-10 = 2
Therefore, our cat weighs 2 pounds more than our friend's.
