Shannon needs 20g of 80% gold to make a pendant. She has some 85% gold and some 70% gold from broken jewellery and wants to know how much of each she should use. Determine the quantity of each alloy that she should use
pls help in 2 mins
To determine the quantities of each alloy Shannon should use, we can set up a system of equations based on the given information.
Let's assume that Shannon needs x grams of the 85% gold alloy and y grams of the 70% gold alloy.
Since the combined quantity of the two alloys should be equal to 20 grams, we have the equation:
x + y = 20 ---(1)
Now, let's consider the gold content in each alloy.
For the 85% gold alloy, the amount of gold is 85% of x grams.
For the 70% gold alloy, the amount of gold is 70% of y grams.
Since Shannon needs a total of 20g of gold (80% gold), we have the equation:
0.85x + 0.70y = 0.80 * 20 ---(2)
Simplifying equation (2), we get:
0.85x + 0.70y = 16
Now, we have a system of two equations:
x + y = 20 ---(1)
0.85x + 0.70y = 16 ---(2)
To solve this system of equations, we can use the substitution or elimination method.
Let's solve it using the elimination method:
Multiply equation (1) by 0.70 to match the coefficients of y:
0.70x + 0.70y = 14 ---(3)
Now, subtract equation (3) from equation (2) to eliminate the y variable:
(0.85x + 0.70y) - (0.70x + 0.70y) = 16 - 14
0.85x - 0.70x = 2
0.15x = 2
x = 2 / 0.15
x ≈ 13.33
Substitute the value of x back into equation (1) to solve for y:
13.33 + y = 20
y = 20 - 13.33
y ≈ 6.67
Therefore, Shannon should use approximately 13.33 grams of the 85% gold alloy and 6.67 grams of the 70% gold alloy to make the pendant.
To determine the quantity of each alloy Shannon should use, we can set up a system of equations based on the information given.
Let's assume Shannon will use x grams of the 85% gold alloy and y grams of the 70% gold alloy.
The first equation can be derived from the fact that Shannon needs a total of 20 grams of 80% gold:
x + y = 20
The second equation can be derived from the requirement of achieving an 80% gold composition. We know that the 85% gold alloy and the 70% gold alloy will combine to form a total of 20 grams, with an overall composition of 80%:
(85% * x + 70% * y) / (x + y) = 80%
Now we have a system of equations:
x + y = 20
(85% * x + 70% * y) / (x + y) = 80%
To solve this system, we can use substitution or elimination. In this case, let's use substitution.
Rearrange the first equation to solve for x:
x = 20 - y
Substitute this value of x into the second equation:
(85% * (20 - y) + 70% * y) / (20 - y + y) = 80%
Simplify and solve for y:
(0.85 * (20 - y) + 0.7 * y) / 20 = 0.8
17 - 0.85y + 0.7y = 16
-0.15y = -1
y = (-1) / (-0.15)
y = 6.67 grams (approximately)
Now substitute this value of y back into the first equation to find x:
x + 6.67 = 20
x = 20 - 6.67
x = 13.33 grams (approximately)
Therefore, Shannon should use approximately 13.33 grams of the 85% gold alloy and approximately 6.67 grams of the 70% gold alloy to make the pendant.
Let x be the weight of 85% gold. Then the rest (20-x) is 70% gold.
So add up the gold in the parts, and it must equal the amount in the final alloy.
0.85x + 0.70(20-x) = 0.80*20
Now solve for s.