SOLUTION: second number is 5 less than the first,thorn number is 1 more than twice the first, if the third number is 20 more than the second what are the three numbers? could you please e

Question 698261: second number is 5 less than the first,thorn number is 1 more than twice the first, if the third number is 20 more than the second what are the three numbers?
could you please explain how to do these type of problems if you can.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
First, designate the 3 number as a, b, c
:
Write a equation for each statement ("is" means =)
:
"second number is 5 less than the first,"
b = a - 5
:
"third number is 1 more than twice the first,"
c = 2a + 1
:
"the third number is 20 more than the second"
c = b + 20
From first statement, we can replace b with (a-5)
c = (a-5) + 20
c = a + 15
From the last statement, we can replace c with (2a+1)
2a + 1 = a + 15
2a - a = 15 - 1
a = 14
then we know b = a - 5, therefore
b = 14 - 5
b = 9
and we know c = b + 20
c = 9 + 20
c = 29
:
Our three numbers: 14, 9, 29
:
:
Confirm this; replace the value in the 3 original equations & see they are true
c = b + 20
c = 9 + 20
c = 29
and
b = a - 5
b = 14 - 5
b = 9
and
c = 2a + 1
c = 2(14) + 1
c = 29
:
There is no set way to do these, the idea is to reduce the number of variables by substitution.
Just keep doing this until there is only one variable in the equation
Then further substitute to find the other variables.
Check your solutions in each statement.

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