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Question 1012391: Good Morning,
HELP!!!! Word problems and methods so confused
!. The perimeter of a rectangular field is 380 yards, the length is 10 yards longer than the width. Find the dimensions. The smaller of the two sides is how many yards.
2. solve the system of equation using the substitution methods.
2x +3y =-2
2x - y = 5
3. Solve using the elimination method.
2r-9s = -43
9r+2s = 19
4. Diabetic express company sells vials of insulin,
Type A at $39.99 and Type B at $30.49.
Collected $1732.62 for 50 vials.
How many of each type was sold.
Thanking you in advance Betty
Found 2 solutions by stanbon, macston:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! !. The perimeter of a rectangular field is 380 yards, the length is 10 yards longer than the width. Find the dimensions. The smaller of the two sides is how many yards.
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P = 2(L + W)
380 = 2(W+10 + W)
190 = 2W + 10
W = 90 yds
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2. solve the system of equation using the substitution methods.
2x +3y =-2
2x - y = 5
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y = 2x-5
2x + 3(2x-5) = -2
----
2x + 6x - 15 = -2
8x = 13
x = 13/8
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Solve for "y"::
y = 2x-5
y = (26/8)
y = 13/4
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Cheers,
Stan H.
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3. Solve using the elimination method.
2r-9s = -43
9r+2s = 19
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18r - 81s = 9*-43
18x + 4s = 2*19
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Subtract and solve for "s"::
85s = 38 + 387
s = 5
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Solve for "r"
2r = 9s - 43
2r = 2
r = 1
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4. Diabetic express company sells vials of insulin,
Type A at $39.99 and Type B at $30.49.
Collected $1732.62 for 50 vials.
How many of each type was sold.
Equations:
Quantity:: n + t = 50 vials
Value:: 39.99n + 30.49t = 1732.62
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3999n + 3999t = 3999*50
3999n + 3049t = 173262
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Subtract and solve for "t":
t = 28.09
Comment:: "t" should be a whole number.
Please check your problem wording.
Cheers,
Stan H.
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Answer by macston(5194)  (Show Source):
You can put this solution on YOUR website! .
1).________________________
W=width; L=length=W+10
.
P=2(L+W)
380=2((W+10)+W)
190=2W+10
180=2W
W=90
ANSWER 1: Width is 90 yards.
L=W+10=90+10=100
ANSWER 2: Length is 100 yards.
.
2)._________________________
2x-y=5
2x=y+5 . Use this to substitute for 2x in other equation:
.
2x+3y =-2
(y+5)+3y=-2
4y=-7
y=-7/4
.
2x-y=5
2x-(-7/4)=5
2x=13/4
x=13/8
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CHECK:
2x+3y=-2
2(13/8+3(-7/4)=-2
13/4-21/4=-2
-8/4=-2
-2=-2
.
3)._____________________
3. Solve using the elimination method.
2r-9s=-43 . Multiply this by 9
9r+2s=19 . Multiply this by 2
.
18r-81s=-387
18r+4s=38 . Subtract to eliminate 18r.
-85s=-425
s=5
.
2r-9s=-43
2r-9(5)=-43
2r-45=-43
2r=2
r=1
.
CHECK:
9r+2s=19
9(1)+2(5)=19
9+10=19
19=19
.
4).___________________________
.
A=vials of Type A; B=vials of Type B
.
A+B=50
A=50-B
.
$39.99A+$30.49B=$1732.62
$39.99(50-B)+$30.49B=$1732.62
$1999.50-$39.99B+30.49B=$1732.62
-$9.50B=-$266.88
B=28.0926315789
There may be an error in this problem as given.
The result should probably be an even number of vials.
.
A=50-B=50-28.0926315789=21.9073684211
.
CHECK:
$39.99A+$30.49B=$1732.62
$39.99(21.9073684211)+$30.49(28.0926315789)=$1732.62
$876.075663158+$856.544336841=$1732.62
$1732.62=$1732.62
.
The problem checks,so it is worked correctly as given.
Usually this type of problem results in whole numbers,
and is not nearly so messy. You may wish to check your
numbers as entered, and using this same method, adjust
your final answer.
.
In the future, please limit to one question per post.
You are more likely to get a response to single questions.
.
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