Algebra
posted by Bob .
three numbers are such that the second is the difference of three times the first and 6 while the third is the sum of 2 and 2/3 the second. The sum of the three numbers is 172. Find the largest number.

n1= first number
n2 = second number
n3 = third number
n2 = 3 n1  6
n3 = 2 + ( 2 / 3 ) n2
n3 = 2 + ( 2 / 3 ) * ( 3 n1  6 )
n3 = 2 + ( 2 / 3 ) * 3 n1  ( 2 / 3 ) * 6
n3 = 2 + 2 n1  4
n3 = 2 n1  2
n1 + n2 + n3 = 172
n1 + 3 n1  6 + 2 n1  2 = 172
6 n1  8 = 172 add 8 to both sides
6 n1  8 + 8 = 172 + 8
6 n1 = 180 Divide both sides by 6
n1 = 180 / 6 = 30
n2 = 3 n1  6
n2 = 3 * 30  6 = 90  6 = 84
n3 = 2 n1  2
n3 = 2 * 30  2 = 60  2 = 58
The largest number = n2 = 84
Respond to this Question
Similar Questions

Algebra I
The sum of three numbers is 147. The second number is 4 more than two times the first number. The third number is five less than three times the first number. Find the three numbers. Can you please solve it? 
algebra
Five times the smallest of three consecutive odd integers is ten more than twice the longest. Find the integers. The sum of three integers is one hundred twenty three more than the first number. The second number is two more than the … 
advance algebra
find three numbers such that the second is 6 less than 3 times the first , and the third is 2 more than 2/3 of the 2nd.The sum of the three numbers is 172. use x=1st number y=second number z= 3rd number please help...thanks a lot!! 
algebra & trigonometry
The sum of three whole numbers is 7. The second number is 1 more than the twice of the third number. The sum of first and third number is 3 less than the second number. Find all the three numbers. Thanks 
algebra & trigonometry
The sum of three whole numbers is 7. The second number is 1 more than the twice of the third number. The sum of first and third number is 3 less than the second number. Find all the three numbers. Thanks 
Algebra (Integer Problem)
The sum of three positive numbers is 33. The second number is 3 greater than the first and the third is 4 times the first. Find the three numbers. 
algebra
Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number. The second number is equal to the sum of the first … 
algebra
Three numbers are such that the first number is 10 less than twice the second and the second number is 4 more than three times the third. Twice the second number is equal to the sum of the first and third numbers. Find the numbers 
mathematicsAlgebra
I think of two whole numbers;the product of the average of the sum and difference of the numbers and the difference of the sum and difference of the numbers is 12.if three times the first added to the second makes up 11..find the two … 
Math
tHE SUM OF THREE NUMBERS IS 75. THE SECOND NUMBER IS 5MORE THAN THE FIRST AND THE THIRD IS THREE TIMES THE SECOND. FIND THE NUMBERS.