SOLUTION: 1. The sum of two numbers is twenty. Three times the smalleris equal to twice the larger. Find the two numbers. 2. A 14-yard fishing line is cut into two pieces. Three times the

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Question 58361: 1. The sum of two numbers is twenty. Three times the smalleris equal to twice the larger. Find the two numbers.
2. A 14-yard fishing line is cut into two pieces. Three times the length of the longer piece is four times the length of the shorter piece. Find the length of each piece.
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) (Show Source):
You can put this solution on YOUR website!
X+Y=20
3X=2Y
X=2Y/3
2Y/3+Y=20
(2Y+3Y)3=20
2Y=3Y=60
5Y=60
Y=60/5
Y=12
X+12=20
X=20-12
X=8
PROOF
3*8=2*12
24=24
8+12=20
20=20
X+Y=14
3X=4Y
X=4Y/3
4Y/3+Y=14
(4Y+3Y)/3=14
7Y=42
Y=42/7
Y=6
X+6=14
X=14-6
X=8
PROOF
4*6=3*8
24=24

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1. The sum of two numbers is twenty. Three times the smalleris equal to twice the larger. Find the two numbers.
Let "x" be the smaller number.
Since 3(x)=2(larger), larger = (3/2)x
EQUATION:
x+(3/2)x=20
(5/2)x=20
x=8 (smaller number)
(3/2)x=12 (larger number)
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2. A 14-yard fishing line is cut into two pieces. Three times the length of the longer piece is four times the length of the shorter piece. Find the length of each piece.
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Let the shorter piece be "x".
Since 3(longer)=4x, longer = (4/3)x
EQUATION:
x+(4/3)x=14
(7/3)x=14
x=6 yrds.(smaller)
(4/3)x=(4/3)6=8 yrds. (larger piece)
Cheers,
Stan H.