Question 1107466
x is the number of grams of 45% copper.
y is the number of grams of 25% copper.
these are melted together to produce 1530 grams of 29% copper.



you get x + y = 1530


you get .45 * x + .25 * y = .29 * 1530.


these two equations need to be solved simultaneously.


leave the first equation as is and multiply both sides of the second equation by 4 to get:


x + y = 1530
1.8 * x + y = 4 * .29 * 1530


simplify the second equation and leave the first equation as is to get:


x + y = 1530
1.8 * x + y = 1774.8


subtract the first equation from the second to get:


.8 * x = 244.8


solve for x to get x = 244.8 /.8 = 306


since x + y = 1530, and x = 306, solve for y to get y = 1530 - 306 = 1224.


it appears that 306 grams of 45% copper and 1224 grams of 25% copper are combined to make 1530 grams of 29% copper.


to confirm this is true, replace x and y in the original equations to see if they are true.


the original equations are:


x + y = 1530
.45 * x + .25 * y = .29 * 1530


replacing x and y with their respective values gets you:


306 + 1224 = 1530 becomes 1530 = 1530 which is true.


.45 * 306 + .25 * 1224  = .29 * 1530


simplify to get 137.7 + 306 = 443.7


simplify further to get 443.7 = 443.7 which is true.


both original equations are true when you replace x with 306 and y with 1224.


this confirms the solution is correct.


the solution is that 1224 grams of 25% copper were mixed with the 45% copper metal.