Answer:
250 kg of 17% and 150 kg of 25%
Step-by-step explanation:
For answering this, we do it by proportions.
take the difference
17% === 20% === 25%
3 5
Then ratio
17% :25% = 5:3
For 400 kg,
17% = 5/(5+3) * 400 = 250 kg
25% = 3/(5+3) * 400 = 150 kg.
Above is a mental method, no calculation or pencil need.
I will edit to give an algebraic method.
Algebraic method:
Given:
17% rods and 25% rods.
Need to make 400 kg of 20% rods.
Let
A=weight of 17% rods
B=weight of 25% rods
to make 20% rods, we need
( 0.17A + 0.25B ) / (A+B) = 0.20 ............(1)
But we know that
A+B=400 .............(2)
substitute
B=400-A in (1)
( 0.17A + 0.25 (400-A) ) / 400 = 0.20
Cross multiply and simplify
(0.17-0.25)A +100 = 80
-0.08A = -20
A = -20 / (-0.08)
A = 250 ...........(3) (17% rods)
substitute (3) in (2)
B = 400-250 = 150 (25% rods)
Same answer as mental calculations
Even simpler albebra, same answer!
Given:
17% rods and 25% rods.
Need to make 400 kg of 20% rods.
Let
W=weight of 25% rods
400-W = weight of 17% rods
To make 20% purity rods, we need to have 400*0.2=80 kg of pure metal, which is
0.25W + 0.17(400-W) = 80
Expand and simplify
0.25W + 68 - 0.17W = 80
0.08W = 80-68 = 12
W = 12/0.08 = 150 (25% rods)
400-W = 250 kg (17% rods)
