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Math Money Problem Please Help?

Ernest and Gene have been saving coins every day for a sunny day in Arizona. Ernest has 8 more half dollars than Gene and no quarters. Gene has as many quarters as Ernest has half dollars, and each has 45 dimes. How many of each coin has each saved for the big day when $200 has been saved?

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  • 1 decade ago
    Favorite Answer

    Let:

    He = number of half-dollars that Ernest has = Hg + 8

    Hg = number of half-dollars that Gene has

    H = total number of half-dollars = He + Hg = (Hg + 8) + Hg = 2Hg + 8

    Qe = number of quarters that Ernest has = 0

    Qg = number of quarters that Gene has = He = Hg + 8

    Q = total number of quarters = Qe + Qh = 0 + Hg + 8 = Hg + 8

    D = total number of dimes = 2(45) = 90

    Equation:

    0.5H + 0.25Q + 0.10(90) = 200

    0.5(2Hg + 8) + 0.25(Hg + 8) + 9 = 200

    Hg + 4 + 0.25Hg + 2 + 9 = 200

    1.25Hg + 15 = 200

    1.25Hg = 200 - 15

    1.25Hg = 185

    Hg = 185/1.25

    Hg = 148

    He = Hg + 8 = 148 + 8 = 156

    Qg = Hg + 8 = 148 + 8 = 156

    H = 2Hg + 8 = 2(148) + 8 = 304

    Q = Hg + 8 = 148 + 8 = 156

    D = 90

    Check:

    0.5(304) + 0.25(156) + 0.10(90) = 200

    152 + 39 + 9 = 200

    200 = 200 Yes!

    Answer:

    Therefore, Ernest and Gene have saved: 304 half-dollars, 156 quarters, and 90 dimes.

    Of these, Gene has saved: 148 half-dollars, 156 quarters, and 45 dimes; Ernest has saved: 156 half-dollars, no quarters, and 45 dimes.

  • 1 decade ago

    When I go about solving these type of math problems, it helps for me to draw a picture or diagram or list the information!

    We Know that the total is $200.00

    $200 - ($4.50 x 2) = $191.00 (This accounts for the 45 dimes each)!

    $191.00 - $4.00 = $187.00 (This accounts for the extra 8 half-dollars Ernest has over Gene).

    $187.00 - $2.00 = $185.00 (This accounts for the 8 quarters that Gene has since he has the same amount of quarters as Ernest has in half-dollars and we know that Ernest has atleast 8 half-dollars).

    $185.00 / $1.25 = 148. ( This tells how many 2 half-dollars and 1 quarter ($.50 + $.50 + $.25 = $1.25) go into the remaining amount).

    So $185.00 - (148 x .50) = $111.00 ( This is what's left after counting Ernest's remaining half-dollars.

    $110.50 - (148 x .50) = $37.00 (This is whats left after counting Gene's half-dollars, 8 less than total amount of Ernest's).

    $37 - (148 x .25) = $0.00

    So, we tallying all the numbers of each coin up.

    Ernest has: 45 dimes, (148 + 8 = 156) so 156 half-dollars, 0 quarters.

    Gene has: 45 dimes, 148 half-dollars, and 156 quarters.

    To double check our work, 1st make sure the requirements meet and also add up all the coins to make sure they equal $200.00.

    Ernest: 45 x $.10 = $4.50 + (156 x $.50) = $82.50

    Gene: 45 x $.10 = $4.50 + (148 x $.50) = $78.50 + (156 x $.25) = $117.50

    So $117.50 + $82.50 = $200.00

    So the answer we arrived at is correct because the requirements given in the problem have been met.

  • 1 decade ago

    We'll call Ernest's half dollars X. Gene's half dollars we'll call Y and his quarters Z. Since Ernest has 8 more half dollars than Gene, we can say Y=X+8. Ernest has no quarters but gene has as many quarters as Ernest has half dollars so Z=X.

    Our total equation will be:

    0.50X + 0.50Y + 0.25Z +2(0.10x45)=200

    Replace the Y and the Z with the equations above.

    0.50X + 0.50(X+8) + 0.25X +2(0.10x45)=200

    and solve for X. You can then plug this number into the Y = X + 8 equation and the Z = X equation to find those.

  • Anonymous
    1 decade ago

    Ernest has

    168 Half Dollars

    0 Quarters

    45 Dimes

    Gene has

    160 Half Dollars

    108 Quarters

    45 Dimes

    Hope this helps u

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  • 1 decade ago

    Ernest -

    168 Half Dollars

    0 Quarters

    45 Dimes

    Gene -

    160 Half Dollars

    108 Quarters

    45 Dimes

  • Anonymous
    4 years ago

    11a) F?S / D² (as a effect)? F=KS / D² b) F=ok½S / 2nd² ? F=ok½S / 4D² think: F=½ 2 / 4 ? F=a million / 4 Then: F=a million / 2&activities;4 Which Equals F=a million / 8 this skill that F is better by skill of way of ? or in different words F is chop up by skill of skill of 8. Can look in basic terms a splash puzzling :/ desire this helped :)

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