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A newspaper vendor receives a salary of [tex]$\$[/tex]35[tex]$ per fortnight plus 20 cents for each newspaper sold. How many papers must he sell to make $[/tex]\[tex]$65$[/tex] fortnightly?
We need to find out how many newspapers a vendor must sell to make [tex]$65 in a fortnight, given that he receives a base salary of $[/tex]35 and earns an additional [tex]$0.20 for each newspaper sold.
1. Identify the components of the vendor's total earnings:
- Base salary: $[/tex]35 - Earnings per newspaper: [tex]$0.20
- Target earnings: $[/tex]65
2. Set up the equation for total earnings:
The total earnings can be represented by combining the base salary and the earnings from the newspapers sold.
[tex]\[
\text{Total earnings} = \text{Base salary} + (\text{Number of newspapers sold} \times \text{Earnings per newspaper})
\][/tex]
Plugging in the known values:
[tex]\[
65 = 35 + (x \times 0.20)
\][/tex]
where [tex]\( x \)[/tex] is the number of newspapers sold.
3. Isolate the term involving [tex]\( x \)[/tex]:
Subtract the base salary from both sides of the equation:
[tex]\[
65 - 35 = 0.20x
\][/tex]
Simplify the left side:
[tex]\[
30 = 0.20x
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
Divide both sides by the earnings per newspaper (0.20) to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{30}{0.20}
\][/tex]
Simplify the division:
[tex]\[
x = 150
\][/tex]
5. Conclusion:
The vendor must sell 150 newspapers to make $65 fortnightly.
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