 Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
`        Find the number of ordered triplets = b, c of positive integers such that 30a + 50b + 70 C is equal to or less than 343`
3 months ago

```							obviously c cant be more than 4, as 70c would become greater than equal to 350.so c can be 1, 2, 3, 4but c also cannot be 4, because if c=4, then 30a + 50b would have to be less than or equal to 343 – 280= 63, but the minimum value of 30a + 50b is 30+50= 80so c can only be 1, 2, 3.when c=3, 30a + 50b should be less than or equal to 343 – 210= 133. in this case, when b=2, a=1 and when b=1, a can be 1, 2.when c=2, 30a + 50b should be less than or equal to 343 – 140= 203. in this case, when b=3, a=1, when b=2, a can be 1, 2, 3 and when b=1, a can be 1,2,3,4,5when c=1, 30a + 50b should be less than or equal to 343 – 70= 273. in this case, when b=4, a=1, 2, when b= 3, a= 1,2,3,4, when b=2, a=1,2,3,4,5 and when b=1, a=1,2,3,4,5,6,7.these are all the possible triplets. the key insight here was to begin with the variable having the largest coeffcient (in this case c with coeff 70).you can count all these triplets and if i have counted them right then number of ordered triplets= 30kindly approve :)
```
3 months ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »  ### Course Features

• 731 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions