assume that a jeweler needs 80 grams of an alloy that is 30% gold. He has avaliable one alloy that is 5% gold and another that is 85% gold; he will mix some of each If x equal the number of grams of the first alloy (so the number of grams of the second is 80-x), find x

solve

.05x + .85(80-x) = .3(80)

To find the value of x, we need to set up an equation based on the given information.

Let's assume that x represents the number of grams of the first alloy (which is 5% gold). We also know that the jeweler needs a total of 80 grams of the alloy.

Therefore, the number of grams of the second alloy (which is 85% gold) would be (80 - x) because the total amount of alloy is 80 grams.

Now, let's calculate the amount of gold in the first alloy:
The first alloy is 5% gold, so 0.05x grams of gold are present in the first alloy.

Similarly, let's calculate the amount of gold in the second alloy:
The second alloy is 85% gold, so 0.85(80 - x) grams of gold are present in the second alloy.

The total amount of gold required for the final alloy is 30% of 80 grams, which is 0.3 * 80 = 24 grams.

Based on the above information, we can set up the equation:
0.05x + 0.85(80 - x) = 24

Now, let's solve this equation for x.

0.05x + 0.85(80 - x) = 24
0.05x + 68 - 0.85x = 24
-0.8x + 68 = 24
-0.8x = 24 - 68
-0.8x = -44
x = -44 / -0.8
x = 55

Thus, the number of grams of the first alloy (x) is 55 grams.