*fan and medal awarded*
The three Math Idol judges have been eliminating contestants all day! The number of one-step equations and two-step equations who have been eliminated today is equal to 1070! If three times the number of one-step equations minus twice the number of two-step equations is equal to 110, how many one-step equations auditioned today?
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This answer will only tell you the number of one-step equations that have been eliminated.
We don't actually know how many auditioned.
Also, be careful with the use of ! in mathematics as 1070! = 1070 x 1069 x 1068 x.......x 3 x 2 x1
Let A be the number of one-step equations eliminated and B the number of two-step equations eliminated then,
A + B = 1070 .....Equation (1)
and we are told that, 3A - 2B = 110.....Equation (2)
multiplying Eqn (1) by 2 gives
2A + 2B = 2140........now add Eqn(2)
3A - 2B = 110
5A = 2250 ⇒ A = 450....which is the number of one-step equations ELIMINATED today.