Question 2 of 14, Step 1 of 1 $1 / 14$ Correct A metallurgist has one alloy containing $22 \%$ titanium and another containing $61 \%$ titanium. How many pounds of each alloy must he use to make 55 pounds of a third alloy containing $28 \%$ titanium? (Round off the answers to the nearest hundredth.) Answer How to enter your answer (opens in new window) Keypad

Step 1 ：Let's denote the amount of the alloy with 22% titanium as \(x\) and the amount of the alloy with 61% titanium as \(y\).

Step 2 ：We know that the total amount of the two alloys should be 55 pounds, so we have the first equation: \(x + y = 55\).

Step 3 ：The total amount of titanium in the third alloy is 28% of 55 pounds, so we have the second equation: \(0.22x + 0.61y = 0.28 \times 55\).

Step 4 ：Solving this system of equations, we find that \(x \approx 46.54\) and \(y \approx 8.46\).

Step 5 ：Final Answer: The metallurgist must use approximately \(\boxed{46.54}\) pounds of the alloy with 22% titanium and approximately \(\boxed{8.46}\) pounds of the alloy with 61% titanium.