The difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find both numbers

Question

The difference of two numbers is 12. Two fifths of the greater number is six more than one third of the lesser number. Find both numbers.

Answer 1

Hi Dyverna,

 

Let the numbers be x and y.

 

x - y = 12  (I assumed that x is greater than y but you can do the opposite, too).

x = 12 + y (We did this so that we could express the number in terms of the other. This is important because we will be dealing with only one variable).

Now, we can use the given information to solve for the number. 

 

2x/5 = (1y/3) + 6

x = 12 + y

(2(12 + y))/5 = (y/3) + 6

(24 + 2y) / 5 = (y/3) + 6  (multiply both sides by 5)

24 + 2y = 5*(y/3) + 30

2y - 5y/3 = 30 - 24

y/3 = 6

y = 18

x = 12 + y

x = 12 + 18

= 30

The numbers are 18 and 30.

 

 

 

Answer 2

Let y = the larger number

Let x = the smaller number

y - x = 12     and 2/5 y= 6 + 1/3 x

y = x + 12    15(2/5 y = 6 + 1/3x)

6y = 90 + 5x

6(x + 12) = 90 + 5x     

6x + 72 = 90 + 5x

x = 18    y - 18 = 12      y = 30