A jar holds 20 coins, each a nickel worth 0.05 dollars or a dime worth 0.10 dollars, and they total 1.60 dollars. How many nickels are there?

1. Let n stand for the number of nickels. 2. Since there are 20 coins in all, the number of dimes is 20 minus n. 3. The nickels are worth 0.05n dollars and the dimes are worth 0.10 times 20 minus n. 4. Adding the two totals gives 0.05n plus 0.10 times 20 minus n equal to 1.60. 5. Expanding the bracket gives 0.05n plus 2 minus 0.10n equal to 1.60. 6. Combining like terms gives negative 0.05n plus 2 equal to 1.60, so negative 0.05n is negative 0.40. 7. Dividing gives n equal to 8, so there are 8 nickels. 8. Checking, 8 nickels give 0.40 dollars and 12 dimes give 1.20 dollars, totalling 1.60 dollars. 9. Answering 12 nickels reports the dime count instead of the nickel count. 10. Answering 16 nickels would make the total only 1.20 dollars, well short of 1.60. _Source: OpenStax Intermediate Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations", section 2.4 Solve Mixture and Uniform Motion Applications_