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?

900

620

520

450

Question

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?

900

620

520

450

texaschic101 · Answer

o = one step equations
t = two step equations

o + t = 1070 ---> t = 1070 - o
3o - 2t = 110

now sub 1070 - o in for t in the 2nd equation
3o - 2t = 110
3o - 2(1070 - o) = 110
3o - 2140 + 2o = 110
5o - 2140 = 110
5o = 110 + 2140
5o = 2250
o = 450

now sub 450 in for o in the 1st equation...
o + t = 1070
450 + t = 1070
t = 1070 - 450
t = 620

450 one step equations auditioned today.