Answer: 490 grams of the first alloy should be used.
30 grams of the second alloy should be used.
Step-by-step explanation:
Let x represent the weight of the first alloy in grams that should be used.
Let y represent the weight of the second alloy in grams that should be used.
A chemist has two alloys, one of which is 15% gold and 20% lead. This means that the amount of gold and lead in the first alloy is
0.15x and 0.2x
The second alloy contains 30% gold and 50% lead. This means that the amount of gold and lead in the second alloy is
0.3y and 0.5y
If the alloy to be made contains 82.5 g of gold, it means that
0.15x + 0.3y = 82.5 - - - - - - - - - - - -1
The second alloy would also contain 113 g of lead. This means that
0.2x + 0.5y = 113 - - - - - - - - - - - - -2
Multiplying equation 1 by 0.2 and equation 2 by 0.15, it becomes
0.03x + 0.06y = 16.5
0.03x + 0.075y = 16.95
Subtracting, it becomes
- 0.015y = - 0.45
y = - 0.45/- 0.015
y = 30
Substituting y = 30 into equation 1, it becomes
0.15x + 0.3 × 30 = 82.5
0.15x + 9 = 82.5
0.15x = 82.5 - 9 = 73.5
x = 73.5/0.15
x = 490
Let us assume the number of children attending the movie = x
Let us also assume the number of adults attending the movie = y
Cost of admission for a children in the movie = $8
Cost of admission of an adult in the movie = $12
Number of people going to the movie on a certain day = 3200
Total amount collected from the movie theater = $33040
Then
x + y = 3200
And
8x + 12y = 33040
2x + 3y = 8260
Let us first take the equation
x + y = 3200
x = 3200 - y
Now we will put the value of x in the equation
2x + 3y = 8260
2(3200 - y) + 3y = 8260
6400 - 2y + 3y = 8260
y = 8260 - 6400
= 1860
Now we will put the value of y from the above deduction in the equation
x + y = 3200
x + 1860 = 3200
x = 3200 - 1860
= 1340
So the number of children going to the movie theater is 1340 and the number of adults going to the movie theater is 1860.
Y=9.25 because inorder to solve this we need to first take 5*.3 which equals 1.5 now that we have this we can move on we now have the equation 1.5 + 2y = 20 so now we need to continue working on getting y by it self so we subtract 1.5 from each side and then that leaves us with 2y=18.5 now we divide by 2 which leaves us with y=9.25 enjoy=)
