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.

$$x+y=11\textrm{ },\textrm{ }10y+x=10x+y-27$$

2.

A collection of nickels and dimes is worth \$23/20. There are 7 more dimes than nickels. How many dimes and how many nickels are there?

$$\frac{x}{20}+\frac{y}{10}=\frac{23}{20}\textrm{ },\textrm{ }y=x+7$$

3.

A fork and knife weigh 6 grams and 8 grams, respectively. If the set contains 13 knives and forks and weighs 84 grams, how many knives and forks are there?

$$x+y=13\textrm{ },\textrm{ }6x+8y=84$$