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 11. If the digits are reversed, the new number is 27 less than the original number. Find the digits in the original number.

\begin{equation}x+y=11\textrm{ },\textrm{ }10y+x=10x+y-27\end{equation}

2.

A collection of nickels and dimes is worth $2. There are 5 more dimes than nickels. How many dimes and how many nickels are there?

\begin{equation}\frac{x}{20}+\frac{y}{10}=2\textrm{ },\textrm{ }y=x+5\end{equation}

3.

A fork and knife weigh 2 grams and 3 grams, respectively. If the set contains 19 knives and forks and weighs 47 grams, how many knives and forks are there?

\begin{equation}x+y=19\textrm{ },\textrm{ }2x+3y=47\end{equation}