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 1150. If three times the number of one-step equations minus twice the number of two-step equations is equal to 1300, how many one-step equations eliminated today?

Answer 1

430

720

1150

1300

Answer 2

Assign variables:

One-step equations: w
Two-step equations: z

Then:
3w - 2z = 1300
and:
w + z = 1150.

Solve for w.

Answer 3

Solving is the part I need help on

Answer 4

Okay, explanation follows:

Answer 5

3w - 2z = 1300
w + z = 1150

Now what we want to do is solve for w, meaning we want z gone. How do we get rid of z? We put w in terms of z, meaning we put z on its own and w on the other side of the equation.

Then:
3w - 2z = 1300

Subtract 3w from both sides:

-2z = 1300 - 3w

Divide by -2:

z = 1.5w - 650

Next:
w + z = 1150

Subtract w from both sides:

z = 1150 - w

Now we want to isolate w so that z is completely gone. Here's how:
First we need to establish that our basis is correct:

z = z

We know z = z, so we can substitute:

1.5w - 650 = 1150 - w

Great! z is gone. Now we can solve for w:
1.5w + w = 1150 + 650
2.5w = 1800
w = 1800/2.5 = 720.