A child's coin bank contains $1.42 in pennies and nickels. If the number of pennies is 38 less than 4 times the number of nickels, how many pennies are in the bank?

So we need to write some equations to solve for the amount of nickels and pennies, which represent our two variables. We know the total amount of nickels and pennies equals $1.42, so we say 0.01P + 0.05N = 1.42. We also know the number of pennies is 38 less than 4 times the number of nickels, so we say P + 38 = 4N. So divide 4 from both sides to get N = 0.25P + 9.5. Plug that into the other equation to get 0.01P + 0.05(0.25P + 9.5) = 1.42. Distribute to get 0.01P + 0.0125P + 0.475 = 1.42. Subtract 0.475 and add the pennies together to get 0.0225P = 0.945. Divide 0.0225 from both sides and P = 42. So there are 42 pennies total in the coin bank.