### Algebra-1 Problems

Problem # |
Problem Statement |
Problems Similar To |
---|---|---|

1. |
The sum of a number and its square is 90. Find the number? |
\begin{equation}x^{2}+x=90\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 (6x+8)*(x+5), while the area of the hole is given by $(x+5)^{2}$. Write an expression for the area (in factored form) of the counter-top that is left after the hole is drilled. |
\begin{equation}(6x+8)(x+5)-(x+5)^{2}\end{equation} |

3. |
Daphne and Stephanie have competing refreshment stand businesses. Daphne's profit can be modeled by the polynomial $x^{2} + 9x + 6$, where 'x' is the number of items sold. Stephanie's profit can be modeled by the polynomial $7x^{2} + 8x + 6$, where 'x' has the same meaning. How much more is Stephanie's profit than that of Daphne's? |
\begin{equation}7x^{2}+8x+6-(x^{2}+9x+6)\end{equation} |

4. |
Area of a circle is 324*$\pi$ sq inches. If the radius is (x - 7), what is the value of 'x'? |
\begin{equation}(x-7)^{2}=324\end{equation} |

5. |
Area of a square is 400. If a side of the square is (10*x - 3) inches long, what is the value of 'x'? |
\begin{equation}(10x-3)^{2}=400\end{equation} |

6. |
A rectangle has one side 10 ft longer than the other, and its area is 144 $ft^{2}$. Find the length of the shorter side of the rectangle. |
\begin{equation}(x+10)x=144\end{equation} |

7. |
A triangular banner has an area of 33 $ft^{2}$. The height of the banner is 5 ft longer than its base. Find the base of the triangle. |
\begin{equation}\frac{1}{2} \times x(x+5)=\frac{66}{2}\end{equation} |