Question

PLEASE HELP!!!!!!!!!!!!
Bonnie has one alloy containing 23% aluminum and another containing 45% aluminum. How many pounds of each alloy must he use to make 58 pounds of a third alloy containing 42% aluminum?

Answer 1

42% of 58=
\[.42\times 58=24.36\] so that is how much you aluminum you want to end up with. put x = amount of first compound which will have 23% of x =
\[.23x\] aluminum. the remainder is 58-x which will have
\[.45(58-x)\] aluminum for a total of
\[.23x+.45(58-x)\] aluminum. set this total to equal 24.36 and get the equation
\[.23x+.45(58-x)=24.36\]

Answer 2

the work now is to solve this equation for x. i would multiply by 100 to clear the decimals and rewrite it as
\[23x+45(58-x)=2436\]

Answer 3

\[23x+2610-45x=2436\]
\[-22x+2610=2436\]
\[-22x=2436-2610\]
\[-22x=-174\]
\[x=\frac{174}{22}\]
\[x=7.9\] rounded

Answer 4

so about 7.9 pounds of the 23% aluminum and about 50.1 of the 45% aluminum. hope steps are clear