Problem Analysis
This problem requires us to find the number of pencils Anushka has, given the counts of erasers, the relationship between pencils and sharpeners, and the total number of items.
- Number of erasers (E) = 4.
- Number of sharpeners (S) is one-fourth the number of pencils (P): $S = \frac{1}{4}P$.
- Total number of items (erasers + pencils + sharpeners) = 49.
Mathematical Setup
We can express the total number of items as an equation:
$E + P + S = 49$Substitute the known value of E:
$4 + P + S = 49$Isolate the terms involving pencils and sharpeners:
$P + S = 49 - 4$ $P + S = 45$Solving for Pencils
Now, substitute the relationship $S = \frac{1}{4}P$ into the equation $P + S = 45$:
$P + \frac{1}{4}P = 45$To solve for P, combine the terms with P:
$\frac{4}{4}P + \frac{1}{4}P = 45$ $\frac{5}{4}P = 45$Isolate P:
$P = 45 \times \frac{4}{5}$ $P = \frac{180}{5}$ $P = 36$Verification
If the number of pencils (P) is 36:
- Number of sharpeners (S) = $\frac{1}{4} \times 36 = 9$.
- Total items = Erasers + Pencils + Sharpeners = $4 + 36 + 9 = 49$.
The calculated total matches the given total, confirming our answer.
Anushka has 36 pencils.
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Important Questions from Linear Equation in 1 Variable
The sum of three fractions A, B, and C, A > B > C, is \(\frac{121}{60}\) . When C is divided by B, the resulting fraction is \(\frac{9}{10}\) , which exceeds A by \(\frac{3}{20}\) . What is the difference between B and C?
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number?
If the measure of one angle of a right triangle is 30° more than the measure of the smallest angle, then the measure of the smallest angle is:
A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?
The sum of three consecutive number is 126. Find the highest number?
