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Sergeeva-Olga [200]
3 years ago
5

What value of x satisfies the equation below? 12 (x − 2) + 3x = 1/2 (x + 6) + 2

Mathematics
1 answer:
kotykmax [81]3 years ago
4 0

Answer:

Step-by-step explanation:

12(x-2)+3x = \frac{1}{2}(x+6)+2\\\\12*x-12*2+3x=\frac{1}{2}x+\frac{1}{2}*6+2\\\\12x - 24+3x =\frac{1}{2}x+1*3+2\\\\15x - 24 = \frac{1}{2}x+3+2\\\\15x-24=\frac{1}{2}x+5\\\\15x-\frac{1}{2}x-24=5\\\\\frac{15*2}{1*2}x-\frac{1}{2}x=5+24\\\\\frac{30}{2}x-\frac{1}{2}x=29\\\\\frac{29}{2}x=29\\\\x=29*\frac{2}{29}\\\\x=2

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D=dimes
n=niclkes
p=pennies
q=quarters

1 dollar (100 cents)
2 times as many nickles as dimes
n=2d

14 more pennies than quarters
p+14=q

and total is 1 dollar so
25q+10d+5n+p=100
ok so we must use logic
the max number of quarters in a dolar is 4
but there are pennies so max is 3
so q=1,2, or 3
therefor p=15,16 or, 17

also, the rest of te coins are only multipules of 5 so the sum amount of pennies and quartes must add to a multiplule of 5

if q=1 and p=15, total is 40 cents
if q=2 and p=16, total is 66 cents
if q=3 and p=17, total is 92 cents
only 40 cents is a multiplule of 10

1 quarter and 15 pennies
now we are having
40 cents is pennies and quartesrs
therfor 100-40=60 cents is nickles and dimes
60=5n+10d
n=2d
sub
60=5(2d)+10d
60=10d+10d
60=20d
divide both sides by 20
3=d
sub
n=2d
n=2(3)
n=6

6 nickles
3 dimes




answer is
1 quarter
3 dimes
6 nickles
15 pennies
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Read 2 more answers
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