How would you solve this?

Question

1000=3000/(20+a)

Please explain each step, because I already know the answer. I just don't understand how to GET the answer. Please try to give me an explanation that I can apply to other math problems of the sort.

Answer 1

1000=3000/(20+a) multiply both sides by (20+a)
1000(20+a) =3000 divide both sides by 1000
20+a=3 sibtract 20 from both sides

a= 3-20 = - 17

Answer 2

1000 = 3000/(20+a)
1000(20 + a) = 3000/(20 + a) * (20 + a)/1
20,000 + 1000a = 3000
20,000 + 1000a - 20,000 = 3000 - 20,000
1000a = -17,000
1000a/1000 = -17,000/1000
a = -17

check:
1000 = 3000/(20 -17)
1000 = 3000/(3)
1000 = 1000

Note:
I saw someone do it like this, and I'll show it more:
1000 = 3000/(20+a)
1000(20 + a) = 3000/(20 + a) * (20 + a)/1
1000(20 + a) = 3000
1000(20 + a)/1000 = 3000/1000
20 + a = 3
20 + a - 20 = 3 - 20
a = -17

Basically, in solving a variable in an equation, you want to isolate the variable, keeping the equation equal by doing the same thing to both sides each time as you get it down to the variable equals a number.
So as you see, when there's a fraction (a division), I would then multiply both sides to cancel the fraction out.

Answer 3

1000=3000/(20+a)

Multiply both sides by (20+a) to get the variable out of a denominator (fractions are ugly)
(20+a)1000=3000

Multiply out the bracket
20 000 + 1000 a = 3000

Isolate 'a' by subtracting 20 000 from each side
1000 a = -17 000

Solve for a by dividing by 1000
a = -17

Answer 4

1000= 3000/(20+a) convert both to fraction form
1000/1= 3000/(20+a) cross multiply to get
3000=1000(20+a) now divide by 1000
3=20+a subract 20 from both sides
3-20=a-20
-17=a

Answer 5

1000=3000/(20+a)

1. cross multiply
1000/1=3000/(20+a)
3000=(1000)(20+a)

2. distribute
3000=20000 +1000a

3. isolate the variable
3000-20000=20000-20000+1000a
-17000=1000a

4. solve for a
-17000/1000=1000a/1000
-17=a

Hope it helps!

Answer 6

first - we all hate fractions & think they should be outlawed. So we get rid of the fraction by multiplying everything by the demoninator (20 + a)

1000 * (20 + a) = 3000

distribute the 1000

1000 * 20 + 1000 * a = 3000
20000 + 1000a = 3000
1000a = -17000
a = -17

Always blow up the fraction this way when you can!

Answer 7

1000=3000/(20+a) ; starting point
1000*(20+a) =3000 ; multiply both side by same quantity
(20+a) = 3000/1000 ;divide both sides by same quantity
20+a = 3 ; simplify
a= -17 ; subtract from both sides by same quantity

Answer 8

1000 (20 + a) = 3000
20 + a = 3
a = 3 - 20
a = - 17

Answer 9

use the backwards method
1. Write 1000 on your paper
2. on the left hand side write what you do to a first (add 20)
3. below that write what you do to it next (3000 divided by it)
4. below that write a (in the middle)
5. on the write hand side write what you would do to reverse each operation (divide-multiply, add-subtract, vice versa)
6. do the reversing operations
7. plug your answer in to check it