if 1/4 of a number is added to1/3 of that number, the result is 15 greater than half of that number. find the number
Answers
Answer:
180
Step-by-step explanation:
If the number is x:
Then as per question:
- x/4+x/3=15+x/2
Bring numbers into common denominator of 12:
- 3x/12+4x/12-6x/12=15
- x/12=15
- x=12*15
- x=180
Answer: 180
Answer: Number is 180
Step-by-step explanation:
Step 1: Lets take the number as x
Step 2: it is said that 1/4 of the number is added to 1/3 of the number.
Which makes out mathematical statement: x/4 + x/3
Step 3: it is said that the sum of x/4 + x/3 results to 15 greater than half of the number.
This makes out mathematical equation as: x/4 + x/3 = 15 + x/2
Step 4: Solving for x
Step 4.1: Transposing x/2 to LHS from RHS
x/4 + x/3 - x/2 = 15 (+ sign changes to - when taken to the other side)
Step 4.2: Equalising the denominators by LCM method
To make the denominators equal, we find out the LCM of the denominators 2, 3 and 4 which equals to 12.
So Multiply x/4 by 3, x/3 by 4 and -x/2 by 6
So our new equation is 3x/ 12 + 4x/12 - 6x/12 = 15
Step 4.3: Add & Subtract Like fractions using BODMAS
Next step is to add the like fractions first (Addition is before Subtraction in BOMAS So..)
∴ 3x/ 12 + 4x/12 - 6x /12 = 15
∴ 7x/12 - 6x/12 = 15
Now Subtract the like fractions.
∴ x/12 = 15
Step 4.4: Transposing
Since our equation is x/12 = 15, transpose the 12 to the RHS Side
∴ x= 15*12 ( / changes to * while transposing)
∴ x = 180
That's the number, Answer is 180