SOLUTION: mark has twice as many quarters as nickles and 3 more dimes than nickles, he has $4.20 in all, how many of each does he have. we need formula to figure this out, my daughter is hav

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Question 693143: mark has twice as many quarters as nickles and 3 more dimes than nickles, he has $4.20 in all, how many of each does he have. we need formula to figure this out, my daughter is having horrible time with this, and it has been to long for me to remember.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of nickels he has
Let +d+ = the number of dimes he has
Let +q+ = the number of quarters he has
given:
(1) +q+=+2n+
(2) +d+=+n+%2B+3+
(3) +5n+%2B+10d+%2B+25q+=+420+
( the units for this equation is cents , for instance,
$4.20 is 420 cents )
------------------------
At this point it is important to know if you have
enough information to arrive at a solution.
There are 3 unknowns and 3 equations, which
means a solution is possible.
-------------------------
All you have to do is substitute (1) and (2) into (3)
so that the only variable is +n+, then solve
(3) +5n+%2B+10%2A%28+n+%2B+3+%29+%2B+25%2A%282n%29+=+420+
(3) +5n+%2B+10n+%2B+30+%2B+50n+=+420+
(3) +65n+%2B+30+=+420+
Subtract +30+ from both sides
(3) +65n+=+390+
(3) +n+=+6+
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And, since
(2) +d+=+n+%2B+3+
(2) +d+=+6+%2B+3+
(2) +d+=+9+
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Also, since
(1) +q+=+2n+
(1) +q+=+2%2A6+
(1) +q+=+12+
-------------
Mark has 6 nickels, 9 dimes, and 12 quarters
-------------
check answer:
(3) +5n+%2B+10d+%2B+25q+=+420+
(3) +5%2A6+%2B+10%2A9+%2B+25%2A12+=+420+
(3) +30+%2B+90+%2B+300+=+420+
(3) +420+=+420+
OK
(1) +q+=+2n+
(1) +12+=+2%2A6+
(1) +12+=+12+
OK
(2) +d+=+n+%2B+3+
(2) +9+=+6+%2B+3+
(2) +9+=+9+
OK
Hope this helps



Answer by MathTherapy(10858) About Me  (Show Source):
You can put this solution on YOUR website!

mark has twice as many quarters as nickles and 3 more dimes than nickles, he has $4.20 in all, how many of each does he have. we need formula to figure this out, my daughter is having horrible time with this, and it has been to long for me to remember.

Let amount of nickels, quarters and dimes he has, be N, Q, and D, respectively

Based on the given information, Q = 2N, and D = N + 3

From this, the following coin-value equation can be formed:
.05N + .25(2N) + .1(N + 3) = 4.2

.05N + .5N + .1N + .3 = 4.2

.65N + .3 = 4.2

.65N = 4.2 - .3

.65N = 3.9

N, or amount of nickels = 3.9%2F.65, or highlight_green%286%29

Amount of quarters = 2(6), or highlight_green%2812%29

Amount of dimes = 6 + 3, or highlight_green%289%29

You can do the check!!

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