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 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}