Question

If 3a + 5b + 7c = 1.25 k and 2a + b + 3c = 0.75 k,then 7b + 5c is what percentage of k?

Answer 1

Given,

3a + 5b + 7c = 5/4 k ----I

2a + b + 3c = 3/4 k  ------II

Removing a coefficeint by multiplying by 2 to I and 3 to II

10b + 14c = 5/2 k -----III

3b+  9c=  9/4k -----IV

Subtract IV from III we get 7b+5c=1/4 k

Or, (7b+5c) is 25% of k, is the answer.

Answer 2

Answer:

⇒ 7b + 5c is 25% of k  

Step-by-step explanation:

Given data

                3a + 5b + 7c = 1.25 k _ (1)  

                2a + b + 3c = 0.75 k _ (2)  

here we need to find 7b + 5c and percentage of  7b + 5c in k  

(1) × 2  ⇒ 2 ( 3a + 5b + 7c)  = 2 (1.25 k )

                   6a + 10b + 14c = 2.5 k _ (3)

(2) × 3 ⇒  3 ( 2a + b + 3c ) = 3 (0.75 k )

                   6a + 3b + 9c  = 2.25 k _ (4)

subtract (4) - (3)

          ⇒  6a + 10b + 14c - (6a + 3b + 9c) = 2.5 k - 2.25 k  

          ⇒  6a + 10b + 14c - 6a - 3b - 9c  = 0.25 k

          ⇒    7b + 5c = 0.25 k

          ⇒   7b + 5c = $\frac{25}{100}$ (k)         [ 0.25 = 25/100 ]

⇒ 7b + 5c is 25% of k