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?

Answer 1

i should make a template of this
i have seen it maybe 5 times a week for 2 years now

Answer 2

Its from virtual school >.<

Answer 3

Well we can set up the 2 equations we have been given

Let 1 step equations = 'o'
Let 2 step equations = 't'

\[o + t = 1070\]
\[3o - 2t = 110\]

We can solve that top equation for...lets do 't'

\[t = 1070 - o\]

And now we can substitute this into that second equation for 't'

\[3o - 2(1070 - o) = 110\]

and now simplify

\[3o - 2140 + 2o = 110\]

add 2140 to both sides

\[3o - 2140 + 2140 + 2o = 110 +2140\]

\[3o + 2o = 2250\]

Combine like terms

\[5o = 2250\]

Divide both sides by 5

\[o = \frac{ 2250 }{ 5 }\]

What does 'o' equal...?

Answer 4

Way to confuse the blonde...

Answer 5

Lol "I'm blonde too :P" and is that confusing...??

Answer 6

yes! hey i need help with another problem though...mind helpin?

Answer 7

Well, I think we should make sure you have a firm grasp on what happened here first...

Answer 8

Oh lord...

Answer 9

reminds me of a dylan album

Answer 10

So confused...

Answer 11

Lol it's not bad I swear :)

First lets highlight the important parts of the question

"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?"

"The number of one-step equations and two-step equations who have been eliminated today is equal to 1070!"

This means that the sum of both these variables is equal to 1070 right?
Remember how I let one step equations be represented by 'o' and two step represented by 't'?

so this can be written as

o + t = 1070

"If three times the number of one-step equations minus twice the number of two-step equations is equal to 110"

3 times the one steps (3 x o = 3o) minus (-) twice the number of two step (2 x t = 2t) is 110

put altogether

3o - 2t = 110

How you doing so far?

Answer 12

okay

Answer 13

Okay...this is called a system of equations...you have 2 equations to work with ...to solve your problem

o + t = 1070
and
3o + 2t = 110


Now...you cannot possibly solve these equations "as is"....2 unknowns is too much! so what you do...is solve one of these equations...to isolate 1 variable

This is where I showed that I would solve that top equation for 't'

o + t = 1070

to solve for 't'...I want to get 't' by itself.....so it would be t = ....something

so

o + t = 1070

if I subtract an 'o' from both sides...I will only have 't' left on that left side...so I did that

o + t = 1070
-o -o

t = 1070 - o


With me still...?

Answer 14

yup

Answer 15

typo up there should be 3o - 2t = 110...but still...okay you're with me

Answer 16

yup

Answer 17

So...now we have

3o - 2t = 110

and we now know that

t = 1070 - o

Since we know what 't' EQUALS....we can "substitute" this value into our equation for 't'

3o - 2t = 110

after replacing we have

3o - 2(1070 - o) = 110

Now we distribute that -2 into the parenthesis

3o - 2140 + 2o = 110

Still with me?

Answer 18

*I see you have posted another question...Since We were so close to finishing this one...I'll finish it up

We were left with

3o - 2140 + 2o = 110

We want all of our numbers with 'o' on 1 side and every other number on the other side....so combine the 3o + 2o

5o - 2140 = 110

and add 2140 to both sides

5o - 2140 = 110
+2140 +2140

5o = 2250

and then we divide both sides by 5 because we want to solve for just 'o' right? not 5o.....so

5o = 2250
---------
5 5

o = 450

And that would be your answer...I hope you understood this time