Question 698261
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.