
Example: Tim has 11 coins in his pocket that have a total value of $1. If these coins consists of nickels and dimes only, how many of each kind are there? Solution: Let 'n' be the number of nickels and 'd' be the number of dimes. The word problem can be translated into equation n+d=11 There are 5 cents in a nickel and 'n' nickels equals an amount of 5n. There are 10 cents in a dime and 'd' dimes equals to an amount of 10d. The total value is $1 or 100 cents. Another equation that can be written as 5n+10d=100 Solve these two equations for n and d to find the number of nickels n and dimes d n+d=11 implies n = 11  d 5n+10d=100 substituting n = 11  d in the equation 5n+10d=100 5(11  d)+10d=100 55  5d + 10d = 100 55 + 5d = 100 5d = 100  55 5d = 45 d = 9 n = 11  d = 11  9 = 2 Tim has 9 dimes and 2 nickels Verification: substitute value of n and d in the equation n + d = 11 which is 9 + 2 = 11 or substitute value of n and d in the equation 5n+10d=100 which is 5n+10d= 5x2 + 10x9 = 10 + 90 = 100 Example: Kim has 10 coins that total $2.10. The coins are nickels and quarters only. How many of each kind are there? Solution: Let 'n' be the number of nickels and 'q' be the number of quarters. The word problem can be translated into this equation as n+q=10 Another equation that can be written is 5n+25q=210 Solve these two equations for n and q n+q=10 implies that n = 10  q 5n+25q=210 5(10  q)+25q=210 50  5q + 25q = 210 50 + 20q = 210 20q = 160 q = 8 n = 10  q = 10  8 = 2 There are 8 quarters and 2 nickles Example: Lilly has 21 coins that total $4.50. The coins are dimes and quarters only. How many of each kind are there? Solution: Let 'd' be the number of dimes and 'q' be the number of quarters. The word problem can be translated into this equation d+q=21 Another equation that can be written is 10d+25q=450 Solve these two equations for d and q d+q=21 10d+25q=450 d+q=21 implies d = 21  q substituting in the equation 2 we have 10d+25q=450 10(21  q)+25q=450 210  10q + 25q = 450 210 + 15q = 450 15q = 240 q = 16 d = 21  q = 21  16 = 5 Directions: Solve the following word problems. 