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12 Mar 2026, 02:24
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (01:40) correct
20%
(02:32)
wrong
based on 15
sessions
History
Date
Time
Result
Not Attempted Yet
At a stationery shop, each pen costs p cents more than each pencil. If 8 pencils cost the same as 6 pens, how much do two pencils and one pen cost, in cents?
A. 6p
B. 8p
C. 9p
D. 10p
E. 12p
A. 6p
B. 8p
C. 9p
D. 10p
E. 12p
12 Mar 2026, 03:49
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Great algebra word problem! The key concept being tested here is Variable Substitution in Linear Equations.
The trap most students fall into: jumping straight to setting up the equation without clearly defining what each variable represents — especially when the answer choices are all in terms of p.
Step 1 — Define variables clearly.
Let c = cost of each pencil (in cents). Then each pen costs c + p cents (since each pen costs p cents more than each pencil).
Step 2 — Use the given ratio to set up an equation.
"8 pencils cost the same as 6 pens" means:
8c = 6(c + p)
Step 3 — Solve for c in terms of p.
8c = 6c + 6p
2c = 6p
c = 3p
So each pencil costs 3p cents and each pen costs c + p = 3p + p = 4p cents.
Step 4 — Answer the actual question.
"Two pencils and one pen" = 2(3p) + 1(4p) = 6p + 4p = 10p cents.
Answer: D (10p)
Takeaway: when a problem asks for a cost expressed in terms of a given variable, express ALL unknowns in terms of that variable before computing the final answer — this avoids the temptation to pick a wrong answer like 8p or 12p that appear when students misread the ratio direction.
The trap most students fall into: jumping straight to setting up the equation without clearly defining what each variable represents — especially when the answer choices are all in terms of p.
Step 1 — Define variables clearly.
Let c = cost of each pencil (in cents). Then each pen costs c + p cents (since each pen costs p cents more than each pencil).
Step 2 — Use the given ratio to set up an equation.
"8 pencils cost the same as 6 pens" means:
8c = 6(c + p)
Step 3 — Solve for c in terms of p.
8c = 6c + 6p
2c = 6p
c = 3p
So each pencil costs 3p cents and each pen costs c + p = 3p + p = 4p cents.
Step 4 — Answer the actual question.
"Two pencils and one pen" = 2(3p) + 1(4p) = 6p + 4p = 10p cents.
Answer: D (10p)
Takeaway: when a problem asks for a cost expressed in terms of a given variable, express ALL unknowns in terms of that variable before computing the final answer — this avoids the temptation to pick a wrong answer like 8p or 12p that appear when students misread the ratio direction.
12 Mar 2026, 04:16
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kevincan
Pen = Pencil + p
Given that: 8 pencil = 6 pens
Pencil : Pens = 6:8= 3x : 4x
Substituting it , we get : 4x = 3x + p
p = x
Pen costs 4p , while pencil costs 3p.
Two pencils and One pen costs = 2*3p + 4p = 10p
Option D
