word problem help

Question

The sum of 2 numbers is 24. Seven times the smaller number is the same as 5 times the larger number. Find the smaller number. 

Answer 1

That's a great way of looking at this problem. 

One can also take a little bit different approach, instead of multiplying - Add first - solve it as follows:

 

Set up your problem:  The sum is 24

the larger number is 7 times the unknown and

the smaller number is 5 times the unknown...   7x + 5x = 24

Combine like terms:.................................... 12x   = 24

Divide by 12 on both sides of the equals sign . 12x/12 = 24/12

Solve for x ...............................................    x     = 2

 

Now substitute 2 in place of x:   .................   7x + 5x  = 24

                                                              7(2)+5(2)= 24

                                                                14 + 10 = 24

                                                                24     = 24

 

 Now check that each number equals themselves:  

5*14 = 70    and    7*10 = 70 

 

There you have it - 

Two slightly different approaches to solving the same problem. 

Isn't math fun!!!?

Answer 2

Let the smaller number be X

 

Sum of 2 sumbers is 24. So the other number is 24 - X

 

Given that 7*X = 5*(24- X) 

expanding we get

7X = 120 - 5X

taking terms with X on to left hand side ,

 

12 X = 120

or X = 10

 

So the smaller number is 10

 

Check that, the other number is 14 and 7 times 10 is 70 which is same as 5 times 14 . So our calculation is ok.