Question 1185429
let x = the number of ounces of 1% solution.
let y = total number of ounces of 16% solution.


your equations are:


.01x + .4*100 = .16y
x + 100 = y


simplify to get:


.01x + 40 = .16y
x + 100 = y


multiply both sides of the first equation by 100 and leave the second equation as is to get:


x + 4000 = 16y
x + 100 = y


subtract the second equation from the first to get:


3900 = 15y


solve for y to get:


y = 3900 / 15 = 260


confirm that your original equations are correct when you replace y with 260.


the original equations are:


.01x + .4*100 = .16y
x + 100 = y


simplify to get:


.01x + 40 = .16y
x + 100 = y


replace y with 260 to get:


.01x + 40 = .16*260
x + 100 = 260


simplify to get:


.01x + 40 = 41.6
x + 100 = 260


subtract 40 from both sides of the first equation and subtract 100 from both sides of the second equation to get:


.01x = 41.6 - 40
x = 260 - 100


simplify to get:


.01x = 1.6
x = 160


go back to your original equations and replace y with 260 and x with 160 to get:


.01x + 40 = .16y becomes 1.6 + 40 = .16 * 260
x + 100 = y becomes 160 + 100 = 260


simplify to get:


41.6 = 41.6
260 = 260


this confirms the values of x and y are correct.


your solution is that:


x = 160 and y = 260


let x = the number of ounces of 1% solution.
let y = total number of ounces of 16% solution.


this means that 160 ounces of 1% solution are added to 100 ounces of 40% solution to get 260 ounces of 16% solution.


that's your solution.


normally you would want to move all the variables to the left side of the equal sign and all the constants to the right side of the equal sign, but this is not necessary, and in this case, it was preferable to leave them where they were.