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Simpli ed, the above is   4 372 x 4 372 4x 1488 4x 18 18: 18 5 6 30 30 We want this quantity to equal 80 1488 4x 18 80 30   1488 4x 30 18 30 80 30   1488 4x 30 30 18 2400 30 1488 4x 540 2400 2028 4x 2400 2028 2028 4x 372 x 372 4 x 93
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The student needs a 93 on her quiz to raise her average to 80 Coin problems are also common algebra applications Usually the total number of coins is given as well as the total dollar value The question is normally How many of each coin is there Let x represent the number of one speci c coin and put the number of other coins in terms of x The steps involved are: 1 Let x represent the number of a speci c coin; 2 Write the number of other coins in terms of x (this skill was developed in the age problems); 3 Multiply the value of the coin by its number; this gives the total amount of money represented by each coin; 4 Add all of the terms obtained in Step 3 and set equal to the total money value; 5 Solve for x; 6 Answer the question Don t forget this step! It is easy to feel like you are done when you have solved for x, but sometimes the answer to the question requires one more step
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As in all word problems, units of measure must be consistent In the following problems, this means that all money will need to be in terms of dollars or in terms of cents In the examples that follow, dollars will be used Terri has \$1345 in dimes and quarters If there are 70 coins in all, how many of each coin does she have Let x represent the number of dimes Because the number of dimes and quarters is 70, 70 x represents the number of quarters Terri has x dimes, so she has \$010x in dimes She has 70 x quarters, so she has \$0:25 70 x in quarters These two amounts must sum to \$1345 0:25 70 x 13:45 (amount in (amount in dimes) quarters) 0:10x 0:10x 0:25 70 x 13:45 0:10x 17:5 0:25x 13:45 0:15x 17:5 13:45 17:5 17:50 0:15x 4:05 4:05 x 0:15 x 27 Terri has 27 dimes and 70 x 70 27 43 quarters Bobbie has \$154 in quarters, dimes, nickels, and pennies He has twice as many dimes as quarters and three times as many nickels as dimes The number of pennies is the same as the number of dimes How many of each coin does he have Nickels are being compared to dimes, and dimes are being compared to quarters, so we will let x represent the number of quarters Bobbie has twice as many dimes as quarters, so 2x is the number of dimes he has He has three times as many nickels as dimes, namely triple 2x: 3 2x 6x He has the same number of pennies as dimes, so he has 2x pennies How much of the total \$154 does Bobbie have in each coin He has x quarters, each worth \$025, so he has a total of 025x (dollars) in
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quarters He has 2x dimes, each worth \$010; this gives him 0:10 2x 0:20x (dollars) in dimes Bobbie has 6x nickels, each worth \$005 The total amount of money in nickels, then, is 0:05 6x 0:30x (dollars) Finally, he has 2x pennies, each worth \$001 The pennies count as 0:01 2x 0:02x (dollars) The total amount of money is \$154, so 0:25x (amount in quarters) 0:20x (amount in dimes) 0:30x (amount in nickels) 0:02x (amount in pennies) 1:54:
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0:25x 0:20x 0:30x 0:02x 1:54 0:77x 1:54 1:54 x 0:77 x 2 Bobbie has 2 quarters; 2x 2 2 4 dimes; 6x 6 2 12 nickels; and 2x 2 2 4 pennies