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Table with Missing Values
The table below shows the monthly sales figures (in thousands of units) for three product categories (P, Q, R) across three months (Jan, Feb, Mar) for a particular company. Some values are missing, represented by variables. $$\begin{array}{l|ccc|c} \textbf{Category} & \textbf{Jan} & \textbf{Feb} & \textbf{Mar} & \textbf{Total Sales} \\ \hline \text{P} & 120 & A & 140 & 390 \\ \text{Q} & 150 & 180 & B & 480 \\ \text{R} & C & 130 & 160 & D \\ \hline \textbf{Total} & 410 & E & F & G \end{array}$$ Based on the information provided, what is the value of $A + B + C$? A) 440 B) 420 C) 460 D) 400
The correct answer is **B) 420**. To find the value of $A + B + C$, we need to determine the individual values of $A$, $B$, and $C$ by utilizing the provided row and column totals. **Step 1: Determine the value of A (Sales of Product P in Feb).** We use the 'Total Sales' for Category P, which is the sum of sales in Jan, Feb, and Mar for Product P. Sales of P in Jan + Sales of P in Feb + Sales of P in Mar = Total Sales of P $120 + A + 140 = 390$ $260 + A = 390$ Subtract 260 from both sides: $A = 390 - 260$ $A = 130$ **Step 2: Determine the value of B (Sales of Product Q in Mar).** We use the 'Total Sales' for Category Q, which is the sum of sales in Jan, Feb, and Mar for Product Q. Sales of Q in Jan + Sales of Q in Feb + Sales of Q in Mar = Total Sales of Q $150 + 180 + B = 480$ $330 + B = 480$ Subtract 330 from both sides: $B = 480 - 330$ $B = 150$ **Step 3: Determine the value of C (Sales of Product R in Jan).** We use the 'Total Sales' for the Jan column, which is the sum of sales of Products P, Q, and R in Jan. Sales of P in Jan + Sales of Q in Jan + Sales of R in Jan = Total Sales in Jan $120 + 150 + C = 410$ $270 + C = 410$ Subtract 270 from both sides: $C = 410 - 270$ $C = 140$ **Step 4: Calculate A + B + C.** Now that we have the values for A, B, and C, we can sum them up: $A + B + C = 130 + 150 + 140$ $A + B + C = 420$ The final answer is 420.
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