Final answer:
Assuming a corrected version of the question where half the number of $2 notes is equal to the number of $5 notes, there are 105 $5 notes and 210 $2 notes. Multiplying these by their values and adding the totals, we find that the total value of all the notes is $945.
Step-by-step explanation:
The question relates to a problem in algebra where we need to establish a relation between the number of $2 notes and $5 notes, and find the total value of all notes in the bag. Let's call the number of $2 notes 'x' and assume the typo in the question should be read as 'the number of $2 notes is equal to the number of $5 notes'. As there are 315 notes in total, this gives us the equation x + x = 315. Solving this, we find that x = 157.5, but since we can't have half a note, this suggests that there may be an error in the problem as presented.
Assuming the problem meant to say 'half' of the number of $2 notes is equal to the number of $5 notes, we'd have a system of equations:
x + y = 315
x = 2y
Substituting the second equation into the first one gives us 3y = 315, leading to y = 105, the number of $5 notes, and x = 210, the number of $2 notes. Then, to calculate the total value of the notes, we multiply the number of each type of note by their value and add those amounts together:
Total value of $2 notes = 210 x $2 = $420
Total value of $5 notes = 105 x $5 = $525
Total value of all notes = $420 + $525 = $945