### Algebra-1 Problems

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 (4x+8)*(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}(4x+8)(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 $x^{2} + 4x + 6$, where 'x' is the number of items sold. Stephanie's profit can be modeled by the polynomial $6x^{2} + 9x + 10$, where 'x' has the same meaning. How much more is Stephanie's profit than that of Daphne's? |
\begin{equation}6x^{2}+9x+10-(x^{2}+4x+6)\end{equation} |

4. |
Area of a circle is 361*$\pi$ sq inches. If the radius is (x - 5), what is the value of 'x'? |
\begin{equation}(x-5)^{2}=361\end{equation} |

5. |
Area of a square is 361. If a side of the square is (7*x - 4) inches long, what is the value of 'x'? |
\begin{equation}(7x-4)^{2}=361\end{equation} |

6. |
A rectangle has one side 7 ft longer than the other, and its area is 60 $ft^{2}$. Find the length of the shorter side of the rectangle. |
\begin{equation}(x+7)x=60\end{equation} |

7. |
A triangular banner has an area of 35/2 $ft^{2}$. The height of the banner is 2 ft longer than its base. Find the base of the triangle. |
\begin{equation}\frac{1}{2} \times x(x+2)=\frac{35}{2}\end{equation} |