A metal alloy weighing 5kg and containing 22% iron melted and mixed with 12 kg of a different alloy which contains 90% iron. What percent of the resulting alloy is iron?

70%

Step-by-step explanation:

Given the weight of the first alloy as 5kg(22% iron) and the second as 12kg(90% iron:

#First, we find the weight in kgs of the iron in both alloys:

Hence, the weight of iron in the resulting alloy is 11.9kg.

#From the given info,the total mass of the alloy is 5+12=17kg

Therefore, the % of iron is calculated as :

Hence, 70% of the resulting alloy is iron.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: