Q43. - Algebra 1

Question

Determine the equation of the sentence “The product of 3 and the square of g equals the sum of thirty and the product of nine and g”.

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 $3g^2=30+9g$. The correct option is (D).

Step 1. Given information.

The given sentence is:

The product of 3 and the square of g equals the sum of thirty and the product of nine and g.

Step 2. Break the sentence and write an expression.

The expression for the square of g is $g^2$, and the expression for the product of g and 9 is $9\times g$.

So, the product of 3 and $g^2$ is $3g^2$ and the sum of thirty and $9\times g$ is $30+9\times g$.

Step 3. Write the equation.

Since, $3g^2$ equals $30+9\times g$.

Therefore,

$\begin{array}{c}3g^2=30+9\times g\\ =30+9g\end{array}$

This is the required equation.