3 homework

Question

The difference of two positive numbers is 7 . The larger number is twenty-five less than twice the smaller number. Find the numbers.

The numbers are .

Answer 1

This is an opportunity to use Algebra; as ALWAYS in a 'word' problem, write a statement adopting a letter for an unknown:  Let x and y be two positive numbers, x being the larger of them.

 

x - y = 7 is what The difference of two positive numbers is 7 means

 

x = 2y - 25 is what The larger number is twenty-five less than twice the smaller number means

 

SOLVE THE SYSTEM; you can use the second equation to obtain a substitute for y in the first equation, thus leading to solving for y--then plug in this y value into the second equation to solve for x.

 

Methods VERY SIMILAR to this are being taught in your class. Learn well, because there will be a lot of similar problems in math throughout the years.

Answer 2

x and y are positive so x>0, y>0

 

The difference of two positive numbers is 7:

x - y = 7

 

The larger number is 25 less than twice the smaller number:

x = 2y - 25

 

We can substitute 2y-25 into the first equation in place of x

 

2y-25 - y = 7

y - 25 = 7

y = 7 + 25

y = 32

 

x = 2y-25 = 64-25 = 39

 

Your numbers are 32 and 39