Algebra-1 Problems

8.7 Digit/Coin/Weight Problems


Problem #

Problem Statement

Problems Similar To

1.

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}

2.

A collection of nickels and dimes is worth $11/20. There are 1 more dimes than nickels. How many dimes and how many nickels are there?

\begin{equation}\frac{x}{20}+\frac{y}{10}=\frac{11}{20}\textrm{ },\textrm{ }y=x+1\end{equation}

3.

A fork and knife weigh 5 grams and 7 grams, respectively. If the set contains 15 knives and forks and weighs 87 grams, how many knives and forks are there?

\begin{equation}x+y=15\textrm{ },\textrm{ }5x+7y=87\end{equation}