solve linear equation-an alloy of metal 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

if x g is the 25% copper alloy used, then 1000-x g must be the 50% alloy

does the equation

25/100(x) + 50/100(1000-x) = 45/100(1000)
make any sense to you?

To solve this problem, we can set up a system of equations based on the information given.

Let's assume x represents the amount (in grams) of the first alloy (25% copper) used, and y represents the amount (in grams) of the second alloy (50% copper) used.

We are given two pieces of information:

1. The total weight of the alloy is 1000 grams:
x + y = 1000 (Equation 1)

2. The resulting alloy is 45% copper:
(0.25x + 0.50y) / 1000 = 0.45 (Equation 2)

Now, let's solve this system of equations step-by-step.

Step 1: Solve Equation 1 for x:
x = 1000 - y

Step 2: Substitute the value of x into Equation 2:
(0.25(1000 - y) + 0.50y) / 1000 = 0.45

Step 3: Simplify and solve for y:
(250 - 0.25y + 0.50y) / 1000 = 0.45
(250 + 0.25y) / 1000 = 0.45
250 + 0.25y = 0.45 * 1000
250 + 0.25y = 450
0.25y = 450 - 250
0.25y = 200
y = 200 / 0.25
y = 800

Step 4: Substitute the value of y back into Equation 1 to find x:
x = 1000 - y
x = 1000 - 800
x = 200

Therefore, to make 1000 grams of an alloy that is 45% copper, you would need 200 grams of the 25% copper alloy and 800 grams of the 50% copper alloy.

To solve this problem, we can set up a system of linear equations using the information given.

Let's denote the amount of the first alloy (25% copper) as "x" grams, and the amount of the second alloy (50% copper) as "y" grams. Since the total weight of the alloy we want to make is 1000 grams, we have the equation:

x + y = 1000 -- Equation 1

Next, we need to consider the amount of copper in each alloy. The first alloy is 25% copper, so the amount of copper it contains is 0.25x grams. Similarly, the second alloy is 50% copper, so the amount of copper it contains is 0.50y grams. For the final alloy to have a copper concentration of 45%, the amount of copper it contains is 0.45 * 1000 = 450 grams. So, we have another equation:

0.25x + 0.50y = 450 -- Equation 2

Now, we can solve this system of equations.

One way to solve this system is to use the substitution method. Rearrange Equation 1 to solve for x:

x = 1000 - y

Now substitute this value of x into Equation 2:

0.25(1000 - y) + 0.50y = 450

Simplify the equation:

250 - 0.25y + 0.50y = 450

Combine like terms:

0.25y + 0.50y = 450 - 250

0.75y = 200

Divide both sides of the equation by 0.75:

y = 200 / 0.75

y ≈ 266.67 grams

Now substitute this value of y back into Equation 1 to find x:

x + 266.67 = 1000

x = 1000 - 266.67

x ≈ 733.33 grams

Therefore, you would need approximately 733.33 grams of the first alloy (25% copper) and approximately 266.67 grams of the second alloy (50% copper) to make 1000 grams of an alloy that is 45% copper.

Note: Since we are dealing with grams, we can round the values to two decimal places for practical purposes.