bot also answer these questions:
How many ounces of pure silver must be added to 100 ounces, 40% pure, to make an alloy which is 65% pure silver?
A perfumer wishes to blend perfume valued at Php 4.10 an ounce with perfume worth Php 2.50 an ounce to obtain a mixture of 40 ounces worth Php 3.00 an ounce. How much of the Php 4.10 perfume should use?
A gourmet chef blends a salad dressing by mixing 20 ounces of a solution containing 85% olive oil with pure corn oil, in order that the dressing be 50% olive oil. How much corn oil should be use?
What percentage of a mixture of sand, gravel and cement containing 30% cement should be replaced by pure cement in order to produce that is 40% cement?
For the first question:
To find how many ounces of pure silver must be added to 100 ounces, 40% pure, to make an alloy which is 65% pure silver, we can set up an equation based on the amount of pure silver in the initial mixture and the final mixture.
Let x be the number of ounces of pure silver to be added.
In the initial mixture of 100 ounces, 40% of it is pure silver, so we have 0.40 * 100 = 40 ounces of pure silver.
In the final mixture, we have 100 + x total ounces, and we want it to be 65% pure silver. So, we have 0.65 * (100 + x) ounces of pure silver.
Equating the amount of pure silver in the initial and final mixtures, we can write the equation:
40 + x = 0.65 * (100 + x)
Expanding the equation, we get:
40 + x = 65 + 0.65x
Combining like terms, we get:
0.35x = 25
Dividing both sides by 0.35, we find:
x = 71.43
Therefore, approximately 71.43 ounces of pure silver must be added to the initial 100 ounces, 40% pure, to make an alloy which is 65% pure silver.
For the second question:
To determine how much of the Php 4.10 perfume should be used to blend with the Php 2.50 perfume in order to obtain a mixture of 40 ounces worth Php 3.00 an ounce, we can set up an equation based on the value and quantity of the perfumes.
Let x be the amount of the Php 4.10 perfume to be used.
The value of the Php 4.10 perfume used is 4.10x.
The value of the Php 2.50 perfume used is 2.50(40 - x), since the total quantity is 40 ounces and we are using x ounces of the more expensive perfume.
The total value of the mixture is 3.00 * 40 = 120.
Setting up the equation, we have:
4.10x + 2.50(40 - x) = 120
Expanding and simplifying, we get:
4.10x + 100 - 2.50x = 120
Combining like terms, we have:
1.60x = 20
Dividing both sides by 1.60, we find:
x ≈ 12.5
Therefore, approximately 12.5 ounces of the Php 4.10 perfume should be used in order to obtain the desired mixture.
For the third question:
To find out how much corn oil should be used when mixing 20 ounces of a solution containing 85% olive oil, in order to make a dressing that is 50% olive oil, we can set up an equation based on the amount of olive oil in the initial solution and the desired mixture.
Let x be the amount of corn oil to be used.
In the initial solution of 20 ounces, 85% of it is olive oil, so we have 0.85 * 20 = 17 ounces of olive oil.
In the final mixture, we have 20 + x total ounces, and we want it to be 50% olive oil. So, we have 0.50 * (20 + x) ounces of olive oil.
Equating the amount of olive oil in the initial and final mixtures, we can write the equation:
17 = 0.50 * (20 + x)
Expanding the equation, we get:
17 = 10 + 0.50x
Subtracting 10 from both sides, we have:
7 = 0.50x
Dividing both sides by 0.50, we find:
x = 14
Therefore, 14 ounces of corn oil should be used to make the desired dressing.
For the fourth question:
To determine the percentage of the mixture of sand, gravel, and cement that should be replaced by pure cement in order to produce a mixture that is 40% cement, we need to set up an equation based on the amount of cement in the initial mixture and the desired mixture.
Let x be the percentage of the mixture to be replaced by pure cement.
In the initial mixture, 30% of it is cement, so we have 0.30x of cement.
In the final mixture, we want it to be 40% cement, so we have 0.40(100 - x) of cement.
Equating the amount of cement in the initial and final mixtures, we can write the equation:
0.30x = 0.40(100 - x)
Expanding the equation, we get:
0.30x = 40 - 0.40x
Combining like terms, we have:
0.70x = 40
Dividing both sides by 0.70, we find:
x ≈ 57.14
Therefore, approximately 57.14% of the mixture of sand, gravel, and cement should be replaced by pure cement in order to produce a mixture that is 40% cement.