divide 120 into two parts such that when one is divided by 4 and 5, the sum of quotients is 28.
x/4 + (120-x)/5 = 28
times 20 , the LCD
5x + 4(120-x) = 560
5x + 480 - 4x = 560
x = 80
so we split them up as 80 and 40 , with the 80 being divided by 4 and the 40 divided by 5
check:
80/4 + 40/5 = 20+8 = 28
Very helpful to me
THANKING YOU
To solve this problem, we can use algebraic equations.
Let's assume the two parts that you want to divide 120 into are x and y.
According to the problem, we have the following conditions:
1) When x is divided by 4: x/4
2) When x is divided by 5: x/5
The sum of these two quotients is 28, so we can write the equation:
x/4 + x/5 = 28
To simplify this equation, we need to find a common denominator. In this case, the common denominator is 20, so the equation becomes:
5x/20 + 4x/20 = 28
Combining the fractions, we get:
(5x + 4x)/20 = 28
9x/20 = 28
To solve for x, you can cross multiply:
9x = 28 * 20
9x = 560
Divide both sides of the equation by 9 to solve for x:
x = 560 / 9
Now that you have the value of x, you can find the value of y by subtracting x from the total:
y = 120 - x
y = 120 - (560 / 9)
Simplifying this equation, we get:
y = (1080 - 560) / 9
y = 520 / 9
Therefore, the two parts you are looking for are approximately:
x ≈ 62.22
y ≈ 57.78
So, when you divide approximately 62.22 by 4 and 57.78 by 5, the sum of the quotients is approximately 28.