shanon needs 20g of 80% of gold to make a pendan. she has some 85% gold and some 70% gold, from broken jewelry and wants to know how much she should use. determine the quantity of each alloy that she should use.
amount of 85% gold ---> x g
amount of 70% gold ---> 20-x
solve for x :
.85x + .7(20-x) = .8(20)
thanks :)
To determine the quantity of each alloy Shannon should use, we need to set up an equation based on the given information.
Let's assume she needs "x" grams of the 85% gold alloy and "y" grams of the 70% gold alloy.
Based on the given information, we know that the total weight of the gold used should be 20 grams. Therefore, we can write the equation:
x + y = 20 (equation 1)
We also know that the gold content in the 85% gold alloy is 85% of x grams and the gold content in the 70% gold alloy is 70% of y grams. We can set up the equation for the gold content as well:
(85/100) * x + (70/100) * y = 80% * 20
(85/100) * x + (70/100) * y = 0.8 * 20 (equation 2)
Simplifying equation 2, we get:
0.85x + 0.70y = 16 (equation 3)
Now we have a system of equations to solve. We can solve it using any method, but in this case, let's solve it by substitution.
From equation 1, we can express x in terms of y:
x = 20 - y
Substituting this value of x into equation 3:
0.85(20 - y) + 0.70y = 16
17 - 0.85y + 0.70y = 16
0.15y = 16 - 17
0.15y = -1
y = -1 / 0.15
y = 6.67
Since we can't have a fraction of a gram, let's round it to the nearest whole number:
y ≈ 7
Now, substitute the value of y back into equation 1 to find x:
x + 7 = 20
x = 20 - 7
x = 13
Therefore, Shannon should use 13 grams of the 85% gold alloy and 7 grams of the 70% gold alloy to make the pendant.
To determine the quantity of each alloy Shanon should use, we need to set up an equation based on the given information.
Let's assume Shanon uses x grams of the 85% gold alloy and y grams of the 70% gold alloy.
According to the question, Shanon needs a total of 20 grams of gold with an 80% purity level. Therefore, the equation for the gold content is:
0.85x + 0.70y = 0.80(20)
Now, let's simplify the equation:
0.85x + 0.70y = 16
To proceed further, we need an additional piece of information. Can you provide the total quantity of gold alloys available to Shanon?