Answer & Step-by-step explanation:
The formula is given in the middle. You are supposed to insert the value of x into this formula to find the value of y (like in the first given example):
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Answer:
Identity property of multiplication
Step-by-step explanation:
From step 5:
Here, to solve for x so that the variable x stands alone, Alberto uses the identity property of multiplication, which justifies what he has in step 6.
Step 6:
According to the identity property of multiplication, any value you multiply by 1 gives you that same value.
Therefore, 1x = 1 × x = x.
The variable x multiplied by 1 will give you x.
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
Yes that’s correct
14 x 2 =28
28 - 5
=23
5 4/5 is a mixed number of 29/5.
