Question 1207581: how do I find how many dimes he has?
Maurice has 280 coins - all quarters and dimes - won from playing poker. If his winnings
total $49.45, how many dimes does he have?"
and help for this please.
"The perimeter of a triangle is 64 metres. The longest side of the triangle is 3 times the
length of the shortest side, and the third side is 8 metres less than double the length of the
shortest side. Determine the dimensions of all three sides of the triangle."
Found 3 solutions by josgarithmetic, ikleyn, mananth:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
help for this please.
"The perimeter of a triangle is 64 metres. The longest side of the triangle is 3 times the
length of the shortest side, and the third side is 8 metres less than double the length of the
shortest side. Determine the dimensions of all three sides of the triangle."
~~~~~~~~~~~~~~~~~~~
If you stop your analysis there, where @josgarithmetic stopped it, your solution
will be 100% incomplete and 100% incorrect.
As you read the problem, you may see that if x is the length of the shortest side
of the triangle, then
the longest side is 3x,
and the third side is 2x-8.
But such triangle can not exist, since the triangle inequality is violated.
Indeed, the sum of sides x and (2x-8) is 3x-8, and it is SHORTER than the length
of the third side, 3x, while, according to the triangle inequality, it should be LONGER
than the third side.
It means that the problem's condition is SELF-CONTRADICTORY and such a triangle CAN NOT exist.
Solved.
--------------------
The " solution " by @mananth is 100% incorrect.
It is " rotten to the core ", since a triangle with side lengths
12 meters, 16 meters and 36 meters does not exist.
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! Maurice has 280 coins - all quarters and dimes - won from playing poker. If his winnings
total $49.45, how many dimes does he have?"
Let the number of dimes maurice has be d
and quarters be q
Maurice has 280 coins
d+q=280...........................................(1)
his winnings total $49.45
10d+25q=49.45*100.........................(2)
10d+25q=4945
multiply (1) by 10 and subtract from (2)
10d+10q= 2800
10d+25q=4945
15q= 2145
q= 2145/15 = 143
d+q= 280
Therefore d = 280-143=137
Maurice has 137 dimes.
Check
0.25×143+0.10×137=35.75+13.70=49.45
The perimeter of a triangle is 64 metres. The longest side of the triangle is 3 times the
length of the shortest side, and the third side is 8 metres less than double the length of the
shortest side. Determine the dimensions of all three sides of the triangle."
Let x be the longest side ,y be the shortest side and z the third side.
The longest side of the triangle is 3 times the
length of the shortest side,
x=3y ......................................(1)
The third side is 8 metres less than double the length of the
shortest side.
z= 2x-8 ..................................(2)
The perimeter of a triangle is 64 metres (given)
x+y+z= 64
x+(x/3)+(2x-8)=64
x+x/3 +2x-8=64
3x+x/3 = 72
multiply by 3
3x+3x = 216
6x=216
x= 36
x=3y
y=x/3
y = 36/3 = 12
x+y+z= 64
12+36+z= 64
z = 64-48
z= 16
The dimensions of the sides of the triangle are 12 meters, 36 meters, and 16 meters.
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