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14 Mar 2026, 07:11
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B
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:
92% (03:06) correct
8%
(04:23)
wrong
based on 13
sessions
History
Date
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An office furniture store is relocating and has 20 equally priced tables and 50 equally priced chairs. If the store sells all of the tables at a 40% discount and all of the chairs at full price, the total proceeds would be $22,000. If it sells all of the tables and chairs at a 10% discount, the total proceeds would be $27,000. Before the store has a chance to mark down the prices, a customer purchases one table and six chairs at their regular prices.
How much does the customer pay in total?
A) 2,000
B) 2,200
C) 2,400
D) 2,600
E) 2,800
How much does the customer pay in total?
A) 2,000
B) 2,200
C) 2,400
D) 2,600
E) 2,800
14 Mar 2026, 08:17
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Great question — this is a classic Systems of Equations problem dressed up in a discount/pricing context. The trap most students fall into is trying to work backwards from the answer choices instead of setting up the algebra cleanly. Here's the step-by-step:
Key concept tested: Setting up and solving a system of two linear equations.
Let T = full price of one table, C = full price of one chair.
Step 1: Translate Condition 1.
"Tables at 40% discount, chairs at full price → total $22,000"
20 × (0.6T) + 50 × C = 22,000
→ 12T + 50C = 22,000 ... (Equation 1)
Step 2: Translate Condition 2.
"All items at 10% discount → total $27,000"
20 × (0.9T) + 50 × (0.9C) = 27,000
→ 18T + 45C = 27,000 ... (Equation 2)
Step 3: Eliminate one variable.
Multiply Equation 1 by 9: 108T + 450C = 198,000
Multiply Equation 2 by 10: 180T + 450C = 270,000
Subtract Equation 1 from Equation 2:
72T = 72,000 → T = 1,000
Step 4: Solve for C.
Substitute T = 1,000 into Equation 1:
12(1,000) + 50C = 22,000
50C = 10,000 → C = 200
Step 5: Answer the actual question.
Customer buys 1 table + 6 chairs at full price:
1(1,000) + 6(200) = 1,000 + 1,200 = 2,200
Answer: B
Common trap: Many students misread Condition 1 and apply a 40% discount to chairs as well, or forget that "40% discount" means you pay 60% of the price. Always translate "x% discount" as multiplying by (1 − x/100) before writing the equation.
Takeaway: Whenever a PS question gives you two "total cost/revenue" conditions involving two unknown prices, immediately set up two equations and solve — don't try to back-solve from the choices unless the algebra gets messy.
Key concept tested: Setting up and solving a system of two linear equations.
Let T = full price of one table, C = full price of one chair.
Step 1: Translate Condition 1.
"Tables at 40% discount, chairs at full price → total $22,000"
20 × (0.6T) + 50 × C = 22,000
→ 12T + 50C = 22,000 ... (Equation 1)
Step 2: Translate Condition 2.
"All items at 10% discount → total $27,000"
20 × (0.9T) + 50 × (0.9C) = 27,000
→ 18T + 45C = 27,000 ... (Equation 2)
Step 3: Eliminate one variable.
Multiply Equation 1 by 9: 108T + 450C = 198,000
Multiply Equation 2 by 10: 180T + 450C = 270,000
Subtract Equation 1 from Equation 2:
72T = 72,000 → T = 1,000
Step 4: Solve for C.
Substitute T = 1,000 into Equation 1:
12(1,000) + 50C = 22,000
50C = 10,000 → C = 200
Step 5: Answer the actual question.
Customer buys 1 table + 6 chairs at full price:
1(1,000) + 6(200) = 1,000 + 1,200 = 2,200
Answer: B
Common trap: Many students misread Condition 1 and apply a 40% discount to chairs as well, or forget that "40% discount" means you pay 60% of the price. Always translate "x% discount" as multiplying by (1 − x/100) before writing the equation.
Takeaway: Whenever a PS question gives you two "total cost/revenue" conditions involving two unknown prices, immediately set up two equations and solve — don't try to back-solve from the choices unless the algebra gets messy.
14 Mar 2026, 08:45
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12T + 50C = 22,000
18T + 45C = 27,000
LCM of 12 and 18 is 36
36T + 150C = 66,000
36T +90C = 54,000
Subtracting we get
Equals
60C =12,000
C= 200
18T + 45C = 27,000
LCM of 12 and 18 is 36
36T + 150C = 66,000
36T +90C = 54,000
Subtracting we get
Equals
60C =12,000
C= 200
