Algebra-1 Problems

8.7 Digit/Coin/Weight Problems

Problem #

Problem Statement

Problems Similar To


The sum of the digits of a two-digit number is 11. 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=11\textrm{ },\textrm{ }10y+x=10x+y-45\end{equation}


A collection of nickels and dimes is worth $5/4. There are 5 more dimes than nickels. How many dimes and how many nickels are there?

\begin{equation}\frac{x}{20}+\frac{y}{10}=\frac{5}{4}\textrm{ },\textrm{ }y=x+5\end{equation}


A fork and knife weigh 2 grams and 3 grams, respectively. If the set contains 7 knives and forks and weighs 19 grams, how many knives and forks are there?

\begin{equation}x+y=7\textrm{ },\textrm{ }2x+3y=19\end{equation}