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anonymous

  • 5 years ago

A piggy bank contains 50 coins, all of them nickels, dimes, or quarters. The total value of the coins is $5.60, and the value of the dimes is five times the value of the nickels. How many coins of each type are there? a. write the system of equations b.Set up a matrix equation AX=B and solve it.

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  1. amistre64
    • 5 years ago
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    x+y+z = 50 x(.05) + 5x(.05) +z(.25) = 5.60 Does this sound right?

  2. anonymous
    • 5 years ago
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    yes

  3. amistre64
    • 5 years ago
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    .05x +.25x +.25z = 5.60 30x +25z = 560 x = (560 - 25z) - 30 getting warmer?

  4. amistre64
    • 5 years ago
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    its hard to set up a matrix in here :)

  5. anonymous
    • 5 years ago
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    yes thank you

  6. amistre64
    • 5 years ago
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    typo: x = (560 - 25z)/30 is correct

  7. amistre64
    • 5 years ago
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    we can simplify this by factoring out 5 from everything: x = (112 - 5z)/6

  8. anonymous
    • 5 years ago
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    Ok

  9. amistre64
    • 5 years ago
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    z = 50-x-y and y = 5x so z=50-x-5x z = 50 -6x

  10. anonymous
    • 5 years ago
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    my professor wants us to put it into a matrix box, and we're supposed to use a calculator to find the inverse, and the multiply it to get the answer. it's supposed to be a 3 x 3 matrix in the calculator, then multiply it by a 1 x 3 matrix

  11. amistre64
    • 5 years ago
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    we briefed over matrix in class, so I aint to knowledgeable about them. Just what I taught meself

  12. anonymous
    • 5 years ago
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    ok thanks anyway

  13. amistre64
    • 5 years ago
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    I was talking with myself last night, I said self? how can we solve this problem using Georgia Math. Myself replied, by using canadian money :) How many quarters are in 5.60? at most 22 barring any restrictions like nickels and dimes... n + d + q = 50 --------------------------- 1 5 (44) = q>22; no good 2 10 (38) = '' 3 15 (32) = " 4 20 (26) = " 5 25 (20) = maybe 6 30 (14) = maybe 7 35 (8) = maybe 8 40 (2) = maybe 9 45 (0) = to many coins.. Got it narrowed down. Now lets see which ones equal the illusive $5.60: 5 25 (20) = .25 + 2.50 + 5.00 = too much 6 30 (14) = .30 + 3.00 + 3.50 = " 7 35 (8) = .35 + 3.50 + 2.00 = " 8 40 (2) = .40 + 4.00 + .50 = 4.90 (not enough) If I did my Georgia Math correctly, there is no "real" money in the piggy bank....

  14. amistre64
    • 5 years ago
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    But then again, we figured on dimes being 5 times the number of nickels and not 5 times the value of the nickels.... back to the drawing board......

  15. amistre64
    • 5 years ago
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    dimes can only be multiples of .10; which limits our nickels to increments of 2 n $ d$ d = n+d ($) q (odd = "x.x5") --------------------------------- 2 (.10) (0.50) 5 = 7 (0.60) 43 - odd bad 4 (.20) (1.00) 10 = 14 (1.20) 36 - (+9.00) bad 6 (.30) (1.50) 15 = 21 (1.80) 29 - odd bad 8 (.40) (2.00) 20 = 28 (2.40) 22 - (+4.50) bad 10 (.50) (2.50) 25 = 35 (3.00) 15 - odd bad 12 (.60) (3.00) 30 = 42 (3.60) 8 - (+2.00) GOOD!! 14 (.70) (3.50) 35 = 49 (4.20) 1 - odd bad 16 (.80) (4.00) 40 = 56>50 coins After much deliberation and a majority vote of congress we come to the conclusion that the piggy bank holds: 12 nickels 30 dimes and 8 quarters. And should be put into an interest bearing account at 4% compounded monthly for 50 years :)

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