MAybought some books $4.95 totalsome books were 50cents each and some were 35 cents each he got less than 8 books how many books did he buy .how many 50books

Question

how many books did he buy how many were 50cents

 

Answer 1

I think the constraint should read "he got less than 8 of each type of book" 

 

Let X = number of 50 cent books

Let Y = number of 35 cent books  

 

To solve this problem you need to find integer solutions to the equation 

 

50*X + 35*Y = 495  

 

Write down some integer multiples of 50 and 35 to see if we can come up with a combination that adds up to 495 

 

Multiples of 50 are {50, 100, 150, 200, 250, 300, 350}

Multiples of 35 are {35, 70, 105, 140, 175, 210, 245}  

 

Now let's subtract the multiples of 50 from 495 to see if we can match any of the numbers in the multiples of 35 list 

 

495 - (multiples of 50) are {445, 395, 345, 295, 245, 195, 145} 

 

Looks like 245 is a match!  245 = 7*35 and 245 = 495 - 5*50 

 

So he bought 5 books for 50 cents

 

Check:  5*50 + 7*35 = 250 + 245 = 495 cents = $4.95