Which means "30 is the product of 6 and a number b"?
A. [tex]$30=6b$[/tex]
B. [tex]$30 \times 6=b$[/tex]
C. [tex]$30=b-6$[/tex]
D. [tex]$30=6+b$[/tex]
Answer (2)
The problem states that 30 is the product of 6 and a number b.
Translate the statement into an equation: 30 = 6 b .
Compare the equation with the given options.
The correct option is A : 30 = 6 b .
Explanation
Understanding the Problem The problem states that 30 is the product of 6 and a number, which we can call 'b'. We need to identify the equation that correctly represents this statement.
Translating the Statement into an Equation The statement "30 is the product of 6 and a number b" can be translated into an equation. The product of 6 and b means 6 multiplied by b, which is written as 6 b . The statement says that 30 is equal to this product, so the equation is 30 = 6 b .
Comparing with the Options Now, we compare the equation 30 = 6 b with the given options: Option A: 30 = 6 b - This matches our equation. Option B: 30 × 6 = b - This means 30 times 6 equals b, which is not what the statement says. Option C: 30 = b − 6 - This means 30 equals b minus 6, which is not what the statement says. Option D: 30 = 6 + b - This means 30 equals 6 plus b, which is not what the statement says. Therefore, the correct equation is 30 = 6 b .
Final Answer The equation that correctly represents the statement "30 is the product of 6 and a number b" is 30 = 6 b .
Examples
Understanding how to translate word problems into algebraic equations is a fundamental skill in mathematics. For example, if you are trying to determine how many items you can buy with a certain amount of money, and each item has a fixed cost, you can use a similar equation to find the number of items. If you have $30 and each item costs $6, the equation 30 = 6 b helps you find out that you can buy 5 items.
The correct mathematical representation of the statement "30 is the product of 6 and a number b" is given by the equation 30 = 6 b . The selected option is A.
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