To determine how many notebooks Junxiang bought altogether, we follow a detailed, step-by-step analysis:
1. Identifying relationships between costs:
- Let the total amount of money Junxiang has be [tex]\( M \)[/tex].
- Let the cost of one notebook be [tex]\( N \)[/tex].
- Let the cost of one file be [tex]\( F \)[/tex].
2. Equating the cost:
- Given that the cost of 4 files is the same as the cost of one notebook, we have:
[tex]\[
4F = N \implies F = \frac{N}{4}
\][/tex]
3. Spending on notebooks and files initially:
- Junxiang spent [tex]\( \frac{1}{4} \)[/tex] of his total money on notebooks and 40 files.
- Let [tex]\( x \)[/tex] be the number of notebooks he bought initially.
- The equation reflecting this spending is:
[tex]\[
\frac{1}{4} M = xN + 40F
\][/tex]
- Substitute [tex]\( F \)[/tex] with [tex]\( \frac{N}{4} \)[/tex]:
[tex]\[
\frac{1}{4} M = xN + 40 \left( \frac{N}{4} \right)
\][/tex]
- Simplify the equation:
[tex]\[
\frac{1}{4} M = xN + 10N
\][/tex]
[tex]\[
\frac{1}{4} M = N(x + 10)
\][/tex]
4. Expressing total money:
- Multiplying both sides by 4, we get:
[tex]\[
M = 4N(x + 10)
\][/tex]
5. Spending remaining money on notebooks:
- Junxiang used half of the remaining money to buy more notebooks.
- The remaining money after the initial spending is:
[tex]\[
M - \frac{1}{4} M = \frac{3}{4} M
\][/tex]
[tex]\[
\frac{1}{2} \text{ of remaining money } = \frac{1}{2} \times \frac{3}{4} M = \frac{3}{8} M
\][/tex]
- The cost of additional notebooks bought with [tex]\(\frac{3}{8} M\)[/tex] is:
[tex]\[
\frac{3}{8} M = yN
\][/tex]
- Substitute [tex]\( M = 4N(x + 10) \)[/tex]:
[tex]\[
\frac{3}{8} \times 4N(x + 10) = yN
\][/tex]
[tex]\[
\frac{3}{2} N(x + 10) = yN
\][/tex]
[tex]\[
y = \frac{3}{2} (x + 10)
\][/tex]
6. Total notebooks count:
- The total number of notebooks is:
[tex]\[
x + y
\][/tex]
- Substitute [tex]\( y \)[/tex] with [tex]\(\frac{3}{2} (x + 10)\)[/tex]:
[tex]\[
x + \frac{3}{2} (x + 10)
\][/tex]
[tex]\[
x + \frac{3}{2} x + 15
\][/tex]
[tex]\[
\frac{5}{2} x + 15
\][/tex]
7. Assuming a value for [tex]\( x \)[/tex]:
- To get an integer number of notebooks, let [tex]\( x = 2 \)[/tex] be:
[tex]\[
\frac{5}{2} (2) + 15 = 5 + 15 = 20
\][/tex]
Thus, the total number of notebooks Junxiang bought altogether is [tex]\(\boxed{20}\)[/tex].
