Hi.
Here, we need to start by writing an equation that represents the relationship between the price of the book and the price of a pencil. The problem tells us that the book costs three times as much as a pencil. If we use the letter "x" to represent the price of a pencil, then the book is 3x.
Now, we are also told that the price of four pencils plus the price of the book equals 2.50. So:
3x + 4x = $2.50.
7x = $2.50
x = 0.357 = 36 cents
So each pencil costs 36 cents.
If the book costs three times that amount, then the price of the book is $1.08.
Let's check if we got it right:
3x + 4x = $2.50
3 (.36) + 4 (.36) = $2.50
$1.08 + $1.44 = $2.52
There is a discrepancy, but this is because we rounded the price of a pencil from .357 to .36. In fact, if we take into account the difference between the rounded number and the unrounded number, we see where the two cent discrepancy in our answer comes from:
.36 - .357 = .003
3(.003) + 4 (.003) = 2.1 cents
That's pretty much the discrepancy, alright. Remember that we can't have thousands of a dollar (tenths of a cent) in the U.S. money system. So you had to round the number of cents that each pencil costs up to 36 cents.
