Five times a number added to 2/3 of the number gives 102. Find the number.
Answers
Answer:
The number is 18
Step-by-step explanation:
Let the number be x
Five times a number be 5x
2/3 of the number be 2/3*x
Given that:
Five times a number added to 2/3 of the number gives 102.
This gives the equation
5x + 2/3*x = 102
Take x common from the Left hand side
x( 5+2/3) = 102
take LCM of 5 and 2/3 = 3
x(5*3 + 2)/3 = 102
x * 17/3 = 102
x = 102*3/17
x = 18
So, the number is 18.
Cross checking the answer
Putting the value of X in the equation
5x + 2/3*x = 102
x = 18
5* 18 + 2/3 * 18 =102
90 + 12 = 102
102 = 102
LHS = RHS
(Left hand side = Right hand side)
Additional Knowledge
The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more numbers. It is used to find the least common multiple of the denominators of the fractions in order to add or subtract them. It is also used in solving problems related to time and distance. The LCM can be calculated using the prime factorization method, the listing out multiples method
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Answer:
Given that: Five times a number added to 2/3 of the number gives 102. So, the number is 18.
Step-by-step explanation:
Step : 1 Let the number be x
Five times a number be 5x
2/3 of the number be 2/3*x
Given that:
Five times a number added to 2/3 of the number gives 102.
This gives the equation
5x + 2/3*x = 102
Take x common from the Left hand side
x( 5+2/3) = 102
take LCM of 5 and 2/3 = 3
x(5*3 + 2)/3 = 102
x * 17/3 = 102
x = 102*3/17
x = 18
So, the number is 18.
Step : 2 Cross checking the answer
Putting the value of X in the equation
5x + 2/3*x = 102
x = 18
5* 18 + 2/3 * 18 =102
90 + 12 = 102
102 = 102
LHS = RHS
(Left hand side = Right hand side)
Additional Knowledge
Step : 3 The smallest positive integer that is a multiple of two or more numbers is known as the least common multiple (LCM). In order to add or subtract fractions, the least common multiple of their denominators is employed. It is also applied to challenges involving time and distance. The listing out multiples approach and the prime factorization method may both be used to determine the LCM.
Step : 4 The improper fraction 17/3 and the mixed number 5 2/3 are equivalent. Simply multiply the fraction's denominator (3) by the whole number (5) and then add the numerator to the mixed number to get an improper fraction (2). A rational number is one that yields the result -7/12 after being multiplied by 5/2 and 2/3. The figure is 1/2.
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