Question

Lawrence vet commented that her puppy gained 10% in weight since the first visit. write an expression that could be evaluated to show the puppy's current weight. Use a variable to represent the weight of the puppy at the first visit. write the expression in simplest form. if the puppy games another 10% and wait from the current visit to a future visit how much will the puppy weigh? write an expression that could be evaluated to show the puppies future weight. Write the expression in simplest form.

Answer 1

We can construct an expression for the weight of the puppy as follows:

*Since we have that the puppy gained a 10% of its original weight, we can determine that value (or write it) like this:

10% = 0.1, Here, 0.1 is a tenth of a unit, where the unit represents 100%. So, from this we write the expression:

$w=x+0.1x\Rightarrow w=1.1x$

Here w represents the weight and x the original weight of the puppy (First visit the vet), the reason that 0.1 multiplies x is because 0.1 represents 10% of the value it will multiply, for example:

If we want to know 10% of 100 units, we can multiply 100 times 0.1 and we will get the 10%, that is 100*0.1 = 10. Now, if we were to want to know 15% of 100 units we would multiply 0.15 times 100, that is 100*0.15 = 15; and so on.

After this, if the rate the puppy gains weight is the same (Another 10%), we would solve for the function as follows:

$w_1=w+0.1w\Rightarrow w_1=1.1w$

And, since we already know the weight of the puppy the previous visit to the vet, we replace the value as follows:

$\Rightarrow w_1=1.1(w+0.1w)$

Now, we expand:

$\Rightarrow w_1=1.1w+0.11w$$\Rightarrow w_1=1.21x$

So, from this, we have that the weight of the puppy the third visit would be given by the expression previously described.