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 840! If three times the number of one-step equations minus twice the number of two-step equations is equal to 870, how many one-step equations auditioned today?

330

510

520

660

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 840! If three times the number of one-step equations minus twice the number of two-step equations is equal to 870, how many one-step equations auditioned today?

 330

 510

 520

 660

australopithecus · Answer

x + y =840

3(x) - 2(y) = 870

australopithecus · Answer

x is the one step equations
y is the two step equations

australopithecus · Answer

do you follow how I got those equations? The trick is just to write down the equation as you read

australopithecus · Answer

I assume you can solve from here

anonymous · Answer

i still need help.. i am really not good at word problems.

australopithecus · Answer

well do you understand how I got those equations?

anonymous · Answer

yes

australopithecus · Answer

do you know how to use system of equations?

anonymous · Answer

yes i believe so

australopithecus · Answer

then you can solve this problem

anonymous · Answer

i know, but i dont know exactly i what i could do to get the correct answer

australopithecus · Answer

how many one-step equations auditioned today?

x is the number of one step equations

so solve for y
x + y =840 
y = 840 - x

sub into the second equation

3(x) - 2(y) = 870

3(x) - 2(840 - x) = 870

solve for x

australopithecus · Answer

follow?

australopithecus · Answer

when using the system of equations you are simply just finding where two lines intersect.

anonymous · Answer

would it be 3x - 1680 + 2x?

anonymous · Answer

when getting rid of the parenthesis?

australopithecus · Answer

looks right

australopithecus · Answer

I HAVE THE POWER!

anonymous · Answer

would i subtract 2 from 3 or 3 from 2?

australopithecus · Answer

3(x) - 2(840 - x) = 870
3x + (-1)(2)(840 - x) = 870
3x + (-2)(840-x) = 870
3x + (-2)(840) + (-x)(-2) = 870
3x + (-2)(840) + 2x = 870
5x + (-2)(840) = 870
5x +(-2)(840) - (-2)(840) = 870 - (-2)(840)
5x = 870 - (-2)(840)
$$\frac{5x}{5} = \frac{870-(-2)(840)}{5}$$
$$x = \frac{870-(-2)(840)}{5}$$

anonymous · Answer

how would i divide this. sorry i am not good enough for algebra 1

australopithecus · Answer

870 - (-2)(840) is just a number I was too lazy to multiply it out

870 + (-1)(-2)(840)
870 + (2)(840)
870 + 1680
2550

australopithecus · Answer

follow?

australopithecus · Answer

2550/5 = x

australopithecus · Answer

use a calculator if you are allowed if not then just

australopithecus · Answer

do it the long way

anonymous · Answer

510?

australopithecus · Answer

yup

anonymous · Answer

thank you

australopithecus · Answer

yup