How can the number 39 be divided into two parts in order that the sum of 2/3 of one part and 3/4 of the other part is 28?
I will assume that by "divided" you mean split up, and not actual division
let one part be x, then the other is 39-x
so (2/3)x + (3/4)(39-x) = 28
times 12 , the LCD
8x + 9(39-x) = 336
8x + 351 - 9x = 336
-x = -15
x = 15
so parts are 15 and 24
check:
(2/3)(15) = 10
(3/4)(24) = 18 and their sum would be 28, as required
(2/3)x+(3/4)(39_x)=28
8x+9(39_x)/12=28
8x+9(39_x)=28 multiply by 12
8x+351_9x=336
_x=336_351
_x=_15
X=15
To solve this problem, let's assume that one part of the number 39 is 'x'. So the other part would be '39 - x' since the sum of the two parts should equal 39.
According to the problem, the sum of 2/3 of one part ('x') and 3/4 of the other part ('39 - x') is equal to 28.
Mathematically, this means:
(2/3) * x + (3/4) * (39 - x) = 28
To solve this equation, we'll simplify it step by step:
First, let's simplify 3/4 * (39 - x):
(3/4) * (39 - x) = (3 * 39)/4 - (3/4) * x
= 117/4 - (3/4) * x
= 117/4 - (3/4)x
Now, let's substitute the two simplified parts back into the main equation:
(2/3) * x + 117/4 - (3/4)x = 28
To simplify further, let's make sure the equation has the same denominator:
(8/12) * x + 117/4 - (9/12)x = 28
Now, let's combine like terms:
[(8x - 9x) + (117/4)]/12 = 28
Simplifying further:
(-x + 117/4)/12 = 28
Next, let's multiply both sides of the equation by 12 to eliminate the denominator:
12 * (-x + 117/4)/12 = 28 * 12
This results in:
-x + 117/4 = 336
Now, to isolate x, let's subtract 117/4 from both sides:
-x = 336 - 117/4
Next, let's simplify the right side:
-x = (336 * 4 - 117) / 4
Therefore:
-x = 1344 - 117 / 4
-x = 1227 / 4
Finally, to find x, let's divide both sides by -1:
x = -1227 / 4
Thus, one part of the number 39 is -1227/4, and the other part is (39 - x) = 39 - (-1227/4).
To simplify the second part:
39 - (-1227/4) = 39 + 1227/4
Therefore, the two parts can be expressed as:
One part = -1227/4
The other part = 39 + 1227/4