Need Help WIth Algebra Word Problem 2?

Question

Three fourths of a number increased by a second number equals 6. Three fourths of the first number decreased by three times the second number equals -6. What are the two numbers?

Answer 1

3/4x+y=6
3/4x-3y=-6

3/4x=6-y
6-y-3y=-6
6-4y=-6
-4y=-12
y=3

3/4x+3=6
3/4x=3
3x=12
x=4

To check:
3/4(4)+3=?
3+3=6

3/4(4)-3(3)=?
3-9=-6

You know, these really aren't that hard. Follow the pattern for the rest of your homework.

Answer 2

Oh, come ON. Have you learned nothing from the first problem? This problem is identical to it apart from a few differences.

Let the numbers be x and y

(3 * x) / 4 + y = 6 (i) and (3 * x)/4 - 3 * y = -6 (ii)

Multiply both sides by 4

3 * x + 4 * y = 24 and 3 * x - 12 * y = -24 (iii)

3 * x + 4 * y = 24 -> 4 * y = 24 - 3 * x -> 12 * y = 72 - 9 * x

Substitute in (iii)

3 * x - (72 - 9 * x) = -24
3 * x - 72 + 9 * x = -24
12 * x - 72 = -24
12 * x = 48
x = 4

12 * y = 72 - 9 * x -> 12 * y = 72 - 36 = 36
y = 3

Answer 3

Let the two numbers be x and y.
Therefore according to the problem:
3x/4+y=6
and
3x/4-3y= -6

from the first equation we get 3x/4=6-y
Substituting the value of 3x/4 in the second equation we get:

6-y-3y=-6.
or,-4y=-12.
or,y=3.

Therefore 3x/4=3.
or,x=4.

Answer 4

( 3/4 ) A + B = 6
( 3/4 ) A - 3B = -6

( 9/4 ) A + 3B = 18      (multiply by 3)
( 3/4 ) A - 3B = -6
( 12/4 ) A + 0B = 12
3A = 12
A = 4
( 3/4 ) (4) + B = 6
3 + B = 6
B = 3

A = 4
B = 3

Answer 5

Start with something like this:

3/4x + y = 6,
3/4x- 3y = - 6.

Answer 6

.75x + y = 6 and .75x - 3y = -6
.75x + y - 6 = .75x - 3y + 6
(add 6 to both sides)
(subtract .75x from both sides: becomes 0x)
(add 3y to both sides)
4y = 12
y = 3

.75x + 3 = 6
(subtract 3 from both sides)
.75x = 3
(divide both sides by .75)
x = 4
AND
.75x - 9 = -6
(add 9 to both sides)
.75x = 3
(divide both sides by .75)
x = 4

THERFORE:
x = 4
y = 3