Question 133423: The fifth number plus the third number equals fourteen.
The fourth number is one more than the second number.
The first number is one less than twice the second number.
The second number plus the third number equals ten.
The sum of all five numbers is 30.
Found 2 solutions by oscargut, ankor@dixie-net.com:
Answer by oscargut(2103)   (Show Source):
You can put this solution on YOUR website! Let numbers x,y,z,w,t
The fifth number plus the third number equals fourteen.
z+t=14 then
The fourth number is one more than the second number.
w=y+1
The first number is one less than twice the second number.
x=2y-1
The second number plus the third number equals ten.
y+z=10
x+y+z+w+t=30
x=2y-1 then y=(x+1)/2
y+z=10 then z=10-y=10-(x+1)/2=(19-x)/2
w=y+1 then w=(x+1)/2+1=(x+3)/2
z+t=14 then t=14-z=14-(19-x)/2=(9+x)/2
then
x+(x+1)/2+(19-x)/2+(x+3)/2+(9+x)/2=30
2x+x+1+19-x+x+3+9+x=60
4x+32=60
4x=28
x=7
numbers are: 7,4,6,5,8
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Let numbers = a, b, c, d, e
:
Write an equation for each statement, then try to get the numbers in terms of b
:
The fifth number plus the third number equals fourteen.
e + c = 14
:
The fourth number is one more than the second number.
d = b + 1
:
The first number is one less than twice the second number.
a = 2b - 1
:
The second number plus the third number equals ten.
b + c = 10
c = 10 - b
:
The sum of all five numbers is 30.
a + b + c + d + e = 30
:
Using the 1st equation, substitute (10-b) for c and you have:
e + (10-b) = 14
e = b + 14 - 10
e = b + 4
:
Substitute for a, c, d, e, in the total equation, find b:
(2b-1) + b + (10-b) + (b+1)+ (b+4) = 30
total the b's and the numbers and you have;
4b + 14 = 30
4b = 30 - 14
b = 16/4
b = 4
:
Use the other equations to find a, c, d, and e; then check the total
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