What is one number that is two more than a second number. Four times the first is one 1 less than 5 times the second.

Question

word problem that i do not understand at all

Answer 1

Let:

a = first number

b = second number

 

a = b+2  ("two more than second number")

4a = 5b-1  ("Four times first is one less than 5 times second")

 

We have two equations and two unknowns.  One easy approach from here is to notice that the top equation allows us to substitute "b+2" for "a" in the 2nd equation:

4a = 5b-1     (re-wrote 2nd equation)

4(b+2) = 5b-1  (substituted "b+2" for "a")

4b+8 = 5b-1    (multiplied 4 into paren's)

4b+9 = 5b        (added 1 to both sides)

      9 =  b         (subtracted 4b from both sides)

 

b=9 —> a=11 (from 1st eqn)

 

Ans:  the two numbers are 9 and 11.

  

Check:

4*(11) = 44

5*(9)-1 = 44   (ok)

 

and 11 is two more than 9  (ok)