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TechRevive is a shop specializing in refurbished computer equipment. They sell only three items: desktop computers ($500 each), monitors ($250 each), and mouse & keyboard combos ($50 each).
On a busy Saturday, exactly 200 customers made a purchase. Half of the customers purchased at least a desktop computer, 1/4 of the customers purchased at least a monitor, but 1/3 of the customers purchased only a mouse & keyboard combo. Of the customers who bought a desktop computer, 4/5 of them bought at least one other item.
How many customers purchased a desktop computer and a mouse & keyboard combo but not a monitor?
Let’s define seven variables:
• a: customers who purchased only a desktop computer
• b: customers who purchased only a monitor
• c: customers who purchased only a mouse & keyboard combo
• d: customers who purchased a desktop computer and monitor, but not a mouse & keyboard combo
• k: customers who purchased a monitor and mouse & keyboard combo, but not a desktop computer
• m: customers who purchased a desktop computer and mouse & keyboard combo, but not a monitor
• n: customers who purchased all three items
We need to determine the value of m.
Given information:
1. Total customers: a + b + c + d + k + m + n = 200
2. Customers who purchased a desktop: a + d + m + n = 1/2 × 200 = 100
3. Customers who purchased a monitor: b + d + k + n = 1/4 × 200 = 50
4. Customers who purchased only a mouse & keyboard combo: c = 1/3 × 200 = 66.67 (rounded to 67)
5. Customers who bought a desktop and at least one other item: d + m + n = 4/5 × 100 = 80
Steps to solve:
1. From the 4th point, c = 67
2. From the 2nd and 5th points: a = 100 – 80 = 20
3. Substituting known values in the first equation:
20 + b + 67 + d + k + m + n = 200
b + d + k + m + n = 113
4. From the 3rd point: b + d + k + n = 50
5. Subtracting this from the equation in step 3:
m = 113 – 50 = 63
Therefore, 63 customers purchased a desktop computer and a mouse & keyboard combo but not a monitor.