### Algebra-1 Problems

Problem # |
Problem Statement |
Problems Similar To |
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1. |
The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 45 less than the original number. Find the digits in the original number. |
\begin{equation}x+y=9\textrm{ },\textrm{ }10y+x=10x+y-45\end{equation} |

2. |
A collection of nickels and dimes is worth $21/10. There are 6 more dimes than nickels. How many dimes and how many nickels are there? |
\begin{equation}\frac{x}{20}+\frac{y}{10}=\frac{21}{10}\textrm{ },\textrm{ }y=x+6\end{equation} |

3. |
A fork and knife weigh 3 grams and 9 grams, respectively. If the set contains 16 knives and forks and weighs 102 grams, how many knives and forks are there? |
\begin{equation}x+y=16\textrm{ },\textrm{ }3x+9y=102\end{equation} |