Question

Match the sentence with an equation.



One half of g plus thirty-two is as much as the sum of fifteen and six times g.

Multiple choice question.

A)
g2=2(g−10)



B)
12g+32=15+6g



C)
g3=24g+4



D)
3g2=30+9g

Answer 1

The given sentence is, "One half of g plus thirty-two is as much as the sum of fifteen and six times g."

Let's break this down into an equation:

- "One half of g" can be represented as \(\frac{1}{2}g\).
- "plus thirty-two" means we add 32, which gives us \(\frac{1}{2}g + 32\).
- "is as much as" translates to an equal sign (=).
- "the sum of fifteen and six times g" can be expressed as \(15 + 6g\).

Putting this all together, we get the equation:

\[
\frac{1}{2}g + 32 = 15 + 6g
\]

Now, let's compare this with the options provided:

A) \(g^2 = 2(g−10)\)

B) \(12g + 32 = 15 + 6g\)

C) \(g^3 = 24g + 4\)

D) \(3g^2 = 30 + 9g\)

To match our derived equation, we can manipulate option B to see if it fits:

If we multiply the entire equation \(\frac{1}{2}g + 32 = 15 + 6g\) by 12 to eliminate the fraction, we get:

\(12(\frac{1}{2}g) + 12(32) = 12(15) + 12(6g)\)

This simplifies to:

\(6g + 384 = 180 + 72g\)

Reorganizing gives us:

\(6g - 72g = 180 - 384\)

Which simplifies to:

\(-66g = -204\)

This is not necessary for this question since we already confirmed that the equation corresponds better with option B directly in its original form.

Thus, the match for the given sentence is:

**B) \(12g + 32 = 15 + 6g\)**