Math Question-please help me come up with an equation...?

Question

An alloy of metals is 25% copper. Another alloy is 50% copper. How much of each alloy should be used to make 1000 grams of an alloy that is 45% copper? I know that the answer is...200 gr. of the 25% alloy and 800 gr. of the 50% alloy, but I can't come up with an equation to solve it. Any help would be so appreciated!

Thank you all so much for your help.

Answer 1

Let x be the amount (in grams) of the 25% copper alloy, and
let y be the amount of the 50% copper alloy.
Then,
.25x + .50y = .45(1000) and
x + y = 1000.

So, y = 1000-x
then
.25x + .50y = .45(1000)
.25x + .50(1000-x)=450
.25x + 500 - .50x = 450
(.25-.50)x +500 = 450
-.25x = -50 (multiply both sides by -1)
.25x = 50 (multiply both sides by 4)
x=200, then substitute x in to the x + y = 1000 equation
200 + y = 1000
so y = 800. and make sure to label each grams of the appropriate % copper alloy.

Answer 2

Call the amount of the first alloy "a" and the amount of the second alloy "b."
You need two equations, as you have two unknowns.

First, the total amount of alloy in the end is 1000 grams, so a+b=1000
Then, you know the total amount of copper in the end, so .25a + .50b=.45*1000 or .25a + .5b=450
Multiply the second equation through by 4 and you get a+2b=1800
Then a+b=1000 and a+2b=1800, so b must be 800. Referring to the first equation, you get then that a=200.

Answer 3

You can set up a pair of simultaneous equations as follows:

Let x = number of grams of alloy 1
Let y = number of grams of alloy 2

Then x + y = 1000 (equation 1)

Now you can equate the amounts of copper. You know that a quarter of alloy 1 plus a half of alloy 2 combine to give 450g of copper in the new alloy, so:

0.25x + 0.5y = 450 (equation 2)

Multiply equation 2 by 4 to get x = 2y = 1800
Subtract equation 1 from this to give x = 800g and therefore y = 200g

Answer 4

you must be in middle school or something to be doing this.

.25x + .5y = .45(1000)

x + y = 1000

you have 2 variables, so you need two equations to solve it.

Answer 5

x+y=1000
25x+50y=45000
dividing by -25
-x-2y=-1800
adding
-y=-800
y=800
x=200
200 g of 25% and 800g of 50%