how many ounces of a metal containing 42% iron must be combined with 5 ounces of a metal contain 50% iron to form an alloy containing 47% iron?

Let the number of ounces of the first metal (which contains 42% iron) be \( x \).

We know that:
- The first metal contains 42% iron, so the amount of iron in it is \( 0.42x \) ounces.
- The second metal contains 50% iron, and there are 5 ounces of it, so the amount of iron in it is \( 0.50 \times 5 = 2.5 \) ounces.

When these two metals are combined, the total weight of the alloy is \( x + 5 \) ounces, and it contains 47% iron. So, the amount of iron in the alloy is \( 0.47(x + 5) \) ounces.

Setting up the equation for the total amount of iron:

\[
0.42x + 2.5 = 0.47(x + 5)
\]

Now, solve for \( x \):

\[
0.42x + 2.5 = 0.47x + 2.35
\]

Subtract \( 0.42x \) from both sides:

\[
2.5 = 0.05x + 2.35
\]

Subtract 2.35 from both sides:

\[
0.15 = 0.05x
\]

Finally, divide by 0.05:

\[
x = \frac{0.15}{0.05} = 3
\]

So, **3 ounces** of the metal containing 42% iron must be combined with 5 ounces of the metal containing 50% iron to form an alloy containing 47% iron.

Would you like further details or have any questions? Here are some related problems:

1. How much of a metal containing 60% iron must be added to 10 ounces of 30% iron to make an alloy with 45% iron?
2. If 7 ounces of 35% iron are mixed with 3 ounces of pure iron, what is the percentage of iron in the new alloy?
3. What is the percentage of iron in an alloy formed by mixing 4 ounces of 70% iron and 6 ounces of 40% iron?
4. How many ounces of a metal containing 25% iron are needed to mix with 8 ounces of 60% iron to obtain an alloy containing 40% iron?
5. If you have 12 ounces of a metal with 55% iron, how much pure iron should be added to get an alloy containing 65% iron?

**Tip:** When solving mixture problems, always write down the equation that balances the total quantity and the total amount of the substance of interest (e.g., iron) across the mixture.

Learn how to calculate the amount of metal containing 42% iron needed to mix with 5 ounces of metal containing 50% iron to form an alloy with 47% iron. This problem involves mixture and percentage calculations, suitable for students in Grades 9-10.

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