A scientist wants to combine two metal alloys into 20 kg of a third alloy which is 60% aluminum. He plans to use one alloy with 45% aluminum content, and a second alloy with 70% aluminum content. How many kilograms of each alloy must be combined?

Number of kg of 45% alum .... x

number of kg of 70% alum .... 20-x

solve for x

.45x + .70(20-x) = .60(20)

(I suggest multiplying each of the 3 term by 100 first)

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

Let's assume the scientist uses "x" kg of the 45% aluminum alloy and "y" kg of the 70% aluminum alloy.

Since aluminum is the focus of the problem, we can set up an equation based on the aluminum content in the resulting alloy:

0.45x + 0.70y = 0.60 * 20

The left side of the equation represents the aluminum content in the two alloys being mixed, and the right side represents the aluminum content of the resulting alloy.

Now, we can set up a second equation based on the total weight of the resulting alloy:

x + y = 20

This equation represents the total weight of the resulting alloy, which is given as 20 kg.

To solve this system of equations, we can use substitution or elimination method. In this case, substitution is more convenient.

Rearranging the second equation to solve for x, we get:

x = 20 - y

Substituting this value of x in the first equation, we have:

0.45(20 - y) + 0.70y = 0.60 * 20

Simplifying and solving for y:

9 - 0.45y + 0.70y = 12

0.25y = 3

y = 3 / 0.25

y = 12

So, the scientist needs to use 12 kg of the 70% aluminum alloy.

Now, substituting this value of y back into the second equation, we can solve for x:

x + 12 = 20

x = 8

Therefore, the scientist needs to use 8 kg of the 45% aluminum alloy and 12 kg of the 70% aluminum alloy to obtain a 20 kg alloy with 60% aluminum content.