I bought three times as many erasers as pens and spent $155 in total. I spent $65 more on the pens than the erasers. Given that 's pen cost $1.90 more than an eraser, find the cost of a pen.
To find the cost of a pen, we need to gather all the information given and break it down step by step.
Let's start by assigning variables. Let's say the cost of an eraser is 'e' dollars and the cost of a pen is 'p' dollars.
We are told that the number of erasers bought is three times the number of pens bought. So, if 'x' is the number of pens bought, then the number of erasers bought is 3x.
We know that the total amount spent is $155. So we can write an equation:
3x(p) + x(e) = 155
We are also told that $65 more was spent on pens than erasers. So we can write another equation:
p - e = 65
Now, the last piece of information given is that the pen cost $1.90 more than an eraser. This can also be written as:
p = e + 1.90
We have three equations:
1) 3xp + xe = 155
2) p - e = 65
3) p = e + 1.90
Now we can solve these equations simultaneously to find the value of 'p', which will give us the cost of a pen.
First, let's solve equation 3) and express 'e' in terms of 'p':
p = e + 1.90
e = p - 1.90
Now, substitute the value of 'e' in equation 2):
p - (p - 1.90) = 65
p - p + 1.90 = 65
1.90 = 65
$1.90 = 65
This is not possible, as $1.90 cannot be equal to $65. There seems to be an inconsistency in the information provided. Please recheck the problem statement or provide any missing information so that we can solve it correctly.