Question

Mick and Mack went to a supermarket and bought boxes of soap detergent. Mack could buy only four boxes, which was \( 1 / 5 \) as much as Mick. How many boxes did Mick buy?

Answer 1

Mick bought 20 boxes of soap detergent, as Mack's purchase of four boxes was
`\( (1)/(5) \)` of Mick's total. This is derived from the equation
`\( 4 = (1)/(5) \cdot M \)` , resulting in
`\( M = 20 \).`

Step-by-step explanation:

In analyzing the scenario, the relationship between Mick and Mack's soap detergent purchases can be expressed algebraically as Mack buying only
`\( (1)/(5) \)` as many boxes as Mick, denoted by the equation
`\( m = (1)/(5) \cdot M \)` . The information further specifies that Mack could only acquire four boxes
`(\( m = 4 \))` .

Combining these details, we form the equation
`\( 4 = (1)/(5) \cdot M \)` . To ascertain the number of boxes Mick bought
`(\( M \))` , we multiply both sides by 5, revealing
`\( M = 20 \)` . Consequently, Mick purchased 20 boxes of soap detergent. This step-by-step approach ensures clarity and precision in solving the problem, aligning with algebraic principles.

The equation not only represents the proportional relationship between Mick and Mack's purchases but also allows for a systematic solution, making the mathematical reasoning transparent for understanding.