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 10. If the digits are reversed, the new number is 54 less than the original number. Find the digits in the original number.

\begin{equation}x+y=10\textrm{ },\textrm{ }10y+x=10x+y-54\end{equation}


A collection of nickels and dimes is worth $47/20. There are 10 more dimes than nickels. How many dimes and how many nickels are there?

\begin{equation}\frac{x}{20}+\frac{y}{10}=\frac{47}{20}\textrm{ },\textrm{ }y=x+10\end{equation}


A fork and knife weigh 2 grams and 6 grams, respectively. If the set contains 13 knives and forks and weighs 38 grams, how many knives and forks are there?

\begin{equation}x+y=13\textrm{ },\textrm{ }2x+6y=38\end{equation}