A no. Plus two-third of itself plus one half of itself plus one-seventh of itself equals 97.find the no.
Ans is42
x + 2x/3 + x/2 + x/7 = 97
x=42
check:
42 + 28 + 21 + 6 = 97
x 2x/3 x/2 x/7=97
x=42
check =42 28 21 6=97
45
To find the number, let's break down the given equation step by step:
1. "A no." (Let's call it x): This is our unknown number.
2. "Plus two-thirds of itself": Multiply x by 2/3.
3. "Plus one-half of itself": Add half of x (x/2).
4. "Plus one-seventh of itself": Add one-seventh of x (x/7).
5. "Equals 97": Set the equation equal to 97.
Now, we can write the equation:
x + (2/3)x + (1/2)x + (1/7)x = 97
To solve this equation, we need to combine like terms and simplify:
Multiply each term by the least common denominator (LCD) to clear the fractions:
(1 + (2/3) + (1/2) + (1/7))x = 97
To add the fractions in the parentheses, we need to find a common denominator. The LCD of 3, 2, and 7 is 42.
(42/42 + (28/42) + (21/42) + (6/42))x = 97
Simplifying the fractions:
(97/42)x = 97
To isolate x, divide both sides of the equation by (97/42):
x = 97 / (97/42)
Dividing by a fraction is the same as multiplying by its reciprocal:
x = 97 * (42/97)
Simplifying the expression:
x = 42
Therefore, the number is 42, as you stated in your answer.