Question

which equation represents the sentence?
the sum of five times a number and seven is equal to twelve.
\textcircled{a} 5n + 7 = 12
\textcircled{b} 5(n + 7) = 12
\textcircled{c} (5n)(7) = 12
\textcircled{d} 5 + n + 7 = 12

which sentence represents the equation?
3x + 4 = 10
\textcircled{a} the sum of three times x and four equals ten.
\textcircled{b} three times the sum of x and four equals ten.
\textcircled{c} the product of three times x and four equals ten.
\textcircled{d} three times the product of x and four equals ten.

Explanation:

First Question

Step1: Analyze each option

• Option A: \(5n + 7=12\). Here, \(5n\) represents five times a number \(n\), and then we add \(7\) (sum), which matches "the sum of five times a number and seven is equal to twelve".
• Option B: \(5(n + 7)=12\) represents five times the sum of a number and seven, not the sum of five times a number and seven.
• Option C: \((5n)(7)=12\) is a product, not a sum.
• Option D: \(5 + n+7 = 12\) represents the sum of \(5\), a number \(n\), and \(7\), not five times a number and seven.

Second Question

Step1: Analyze each option

• Option A: The sum of three times \(x\) (which is \(3x\)) and four (\(+4\)) equals ten (\(=10\)), so \(3x + 4=10\) matches this description.
• Option B: Three times the sum of \(x\) and four would be \(3(x + 4)\), not \(3x+4\).
• Option C: The product of three times \(x\) and four would be \((3x)\times4\), not \(3x + 4\).
• Option D: Three times the product of \(x\) and four would be \(3\times(4x)\), not \(3x + 4\).

Answer:

First Question: A. \(5n + 7 = 12\)
Second Question: A. The sum of three times \(x\) and four equals ten.