Q41. - Algebra 1

Question

Determine the equation of the sentence “A number g to the third power is the same as the product of 24 and g plus 4”.

A. $g^2=2\left(g-10\right)$

B. $\frac{1}{2}g+32=15+6g$

C. $g^3=24g+4$

D. $3g^2=30+9g$

Step-by-Step Solution

Answer

The equation is $g^3=24g+4$. The correct option is (C).

Step 1. Given information.

The given sentence is:

A number g to the third power is the same as the product of 24 and g plus 4.

Step 2. Break the sentence and write an expression.

The expression for number g to the third power is $g^3$, and the expression for the product of 24 and g is $24\times g$.

So, the expression for $24\times g$ plus 4 is $24\times g+4$.

Step 3. Write the equation.

Since, $g^3$ is same as $24\times g+4$.

Therefore,

 $\begin{array}{c}{g}^3=24\times g+4\\ =24g+4\end{array}$

This is the required equation.