Algebra-1 Problems

6.8 Problem Solving: Using Equations


Problem #

Problem Statement

Problems Similar To

1.

The sum of a number and its square is 30. Find the number?

\begin{equation}x^{2}+x=30\end{equation}

2.

A rectangular counter-top has a hole drilled in it to hold a cylindrical container (a utensil holder). The area of the entire counter top is given by (8x+9)*(x+4), while the area of the hole is given by $(x+4)^{2}$. Write an expression for the area (in factored form) of the counter-top that is left after the hole is drilled.

\begin{equation}(8x+9)(x+4)-(x+4)^{2}\end{equation}

3.

Daphne and Stephanie have competing refreshment stand businesses. Daphne's profit can be modeled by the polynomial $x^{2} + 9x + 8$, where 'x' is the number of items sold. Stephanie's profit can be modeled by the polynomial $4x^{2} + 4x + 5$, where 'x' has the same meaning. How much more is Stephanie's profit than that of Daphne's?

\begin{equation}4x^{2}+4x+5-(x^{2}+9x+8)\end{equation}

4.

Area of a circle is 256*$\pi$ sq inches. If the radius is (x - 6), what is the value of 'x'?

\begin{equation}(x-6)^{2}=256\end{equation}

5.

Area of a square is 289. If a side of the square is (9*x - 7) inches long, what is the value of 'x'?

\begin{equation}(9x-7)^{2}=289\end{equation}

6.

A rectangle has one side 3 ft longer than the other, and its area is 18 $ft^{2}$. Find the length of the shorter side of the rectangle.

\begin{equation}(x+3)x=18\end{equation}

7.

A triangular banner has an area of 24 $ft^{2}$. The height of the banner is 8 ft longer than its base. Find the base of the triangle.

\begin{equation}\frac{1}{2} \times x(x+8)=\frac{48}{2}\end{equation}