The numbers if nickels and quarters in a bank are in the ratio 23:25. If the coins are worth $7, how mnay of each type are there?

Answer:25 nickels and 23 quarters Step-by-step explanation:The smallest possible integer solution is 23 nickels and 25 quarters. 23×0.05 + 25×0.25 = 1.15 + 6.25 = $7.40. That's already over $7.00. We can't solve the problem as stated unless we use fractional numbers of coins, and that's impossible. Assume the correct ratio is 25/23 Let n = number of nickels and q = number of quarters. Then we have two conditions. (1)                                n/q = 25/23 (2)             0.05n + 0.25q = 7 (3)                                    n = (25/23)q     Multiplied (1) by q (4) 0.05(25/23)q + 0.25q = 7                  Substituted (3) into (1)           0.05435q + 0.25q = 7                  Simplified                           0.3043q = 7                  Combined like terms (5)                                   q = 23              Divided each side by 0.3043                                  n/23 = 25/23         Substituted (5) into (1)                                        n = 25              Divided each side by 23 There are 25 nickels and 23 quarters. Check: (1) 25/23 = 25/23     (2) 0.05×25 + 0.25×23 = 7                                                      1.25 + 5.75 = 7                                                                      7 = 7 OK.