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 12. Find the number?

\begin{equation}x^{2}+x=12\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+5)*(x+6), while the area of the hole is given by $(x+6)^{2}$. Write an expression for the area (in factored form) of the counter-top that is left after the hole is drilled.

\begin{equation}(8x+5)(x+6)-(x+6)^{2}\end{equation}

3.

Daphne and Stephanie have competing refreshment stand businesses. Daphne's profit can be modeled by the polynomial $x^{2} + 4x + 3$, where 'x' is the number of items sold. Stephanie's profit can be modeled by the polynomial $7x^{2} + 10x + 8$, where 'x' has the same meaning. How much more is Stephanie's profit than that of Daphne's?

\begin{equation}7x^{2}+10x+8-(x^{2}+4x+3)\end{equation}

4.

Area of a circle is 196*$\pi$ sq inches. If the radius is (x - 6), what is the value of 'x'?

\begin{equation}(x-6)^{2}=196\end{equation}

5.

Area of a square is 361. If a side of the square is (10*x - 6) inches long, what is the value of 'x'?

\begin{equation}(10x-6)^{2}=361\end{equation}

6.

A rectangle has one side 4 ft longer than the other, and its area is 77 $ft^{2}$. Find the length of the shorter side of the rectangle.

\begin{equation}(x+4)x=77\end{equation}

7.

A triangular banner has an area of 35 $ft^{2}$. The height of the banner is 9 ft longer than its base. Find the base of the triangle.

\begin{equation}\frac{1}{2} \times x(x+9)=\frac{70}{2}\end{equation}