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Question 318765: 1. Sam is 10 years older than Jack. Twice Sam's age subtracted from 6 times Jack's age is 7 more than Jack's age. Find Jack and Sam's age.
2. Separate 65 into two parts such that 3 times the larger will be 6 more than 6 times the smaller. (HINT: let x and 65-x represent your two numbers)
3. Gill has $3.75 is quarters, dimes, and nickels. He has twice as many quarters as dimes and three more dimes than nickels. Find how much of each coin Bill has.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Sam is 10 years older than Jack. Twice Sam's age subtracted from 6 times Jack's age is 7 more than Jack's age. Find Jack and Sam's age.
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Equations:
s = j+10
6j-2s = j+7
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Substitute for "s" and solve for "j".
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2. Separate 65 into two parts such that 3 times the larger will be 6 more than 6 times the smaller. (HINT: let x and 65-x represent your two numbers)
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Equation:
You don't know which is larger so use either as the largest.
3x =6(65-x)+6
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3. Gill has $3.75 is quarters, dimes, and nickels. He has twice as many quarters as dimes and three more dimes than nickels. Find how much of each coin Bill has.
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Equations:
q = 2d
d = n+3
5n + 10d + 25q = 375 cents
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Substitute for "d" and for "n" and solve for "q":
d = q/2
n = d-3 = (q/2)-3
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5[(q/2)-3] + 10(q/2) + 25q = 375
(5/2)q - 15 + 5q + 25q = 375
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Multiply thru by 2 to get:
5q - 30 + 60q = 750
65q = 780
q = 12
d = 6
n = 3
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Cheers,
Stan H.
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