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i.e. he gave 4 notes of Rs. 100, 8 notes of Rs. 50 and 12 notes of Rs. 20. Example Jane has $ 9.60 in coins. If she has 20 more nickels than dimes and 8 times as many quarters as dimes, how many coins of each type does she have ? Solution : Let the number of dimes Jane has in $ 9.60 be x. Then she has (x + 20 ) nickels and 8 x quarters. Setting the data in the table as : Image table Thus we have .10 x + 0.05 (x + 20) + 0.25 (8 x) = 9. 60 Multiplying by 100 throughout 10 x + 5 (x + 20 ) + 25 (8 x) = 960 10 x + 5 x +100 + 200 x = 960 215 x = 960 - 100 215 x = 860 x = 4 So there are 4 dimes, 24 nickels and 32 quarters.
Example George staged a drama for the building fund of his school. He collected $11375 through the sale of tickets of $ 25 and $ 15 each. The total number of tickets sold was 595. Find the number of tickets of each type. Solution : Let x be the number of tickets of $ 25 each. Hence they must have sold (595 - x) tickets of $ 15 each. Total amount collected is $ 11375 \ 25 (x) + 15 (595 - x) = 11375 25 x + 8925 - 15 x = 11375 10 x = 11375 - 8925 10 x = 2450 x = 245 i.e. they sold 245 tickets of $ 25 and 595 - 245 = 350 tickets of $ 15 each. |
9.1 -
Definition and Solving Techniques |