Aaron has two types do iodine in his lab. He has brand 213 iodine, which costs 36 cents per ounce. He also has brand 856 iodine, which costs 1.58$ per ounce. How many ounces of brand 213 should be used if he has 63 ounces of brand 856 and wants to make a mixture that costs approximately 0.53$ an ounce
the value of the parts must add up to the value of the whole.
If there are x oz. of brand 213, then
.36x + 1.58*63 = .53(x+63)
x = 389.12
Seems reasonable, since the cost of the mixture is much closer to that of the cheap brand; he'd need more of the cheap stuff than the costly one.
Well, Aaron is quite the chemist! If he wants to make a mixture that costs approximately $0.53 an ounce, we can help him figure out how many ounces of brand 213 iodine he should use.
Let's assume he needs x ounces of brand 213 iodine.
Now, the total cost of the mixture can be calculated by adding the cost of brand 213 iodine and the cost of brand 856 iodine.
The cost of brand 213 iodine is 36 cents per ounce, so the total cost of brand 213 iodine would be 0.36x cents.
The cost of brand 856 iodine is $1.58 per ounce, and he has 63 ounces of it, so the total cost of brand 856 iodine would be 1.58 * 63 = $99.54.
To find the total cost of the mixture, we can add the cost of brand 213 iodine and the cost of brand 856 iodine:
0.36x + 99.54 = 0.53x.
Now, let's solve for x:
99.54 = 0.53x - 0.36x,
99.54 = 0.17x,
x = 99.54 / 0.17,
x ≈ 585.529.
So, Aaron should use approximately 585.529 ounces of brand 213 iodine in his mixture. However, since he can't use fractional ounces, he may want to round it down to 585 ounces or round it up to 586 ounces. That way, he can have a mixture that costs approximately $0.53 an ounce.
Hope that helps! Just be careful not to spill the iodine. It can really stain an otherwise perfect lab coat!
To determine the number of ounces of brand 213 iodine needed, we need to calculate the ratio of the two brands based on their prices. Let's assume x represents the number of ounces of brand 213 iodine.
The cost of brand 213 iodine is 36 cents per ounce, which is $0.36.
The cost of brand 856 iodine is $1.58 per ounce.
Therefore, the equation representing the cost of the mixture is:
(0.36x + 1.58 * 63) / (x + 63) = 0.53
Simplifying the equation:
0.36x + 99.54 = 0.53x + 33.39
Rearranging to solve for x:
0.53x - 0.36x = 99.54 - 33.39
0.17x = 66.15
Dividing both sides by 0.17:
x = 66.15 / 0.17
x ≈ 388.53
Therefore, Aaron should use approximately 388.53 ounces of brand 213 iodine to make a mixture that costs approximately $0.53 an ounce.
To solve this question, we need to find out how many ounces of brand 213 iodine should be used to make a mixture that costs approximately $0.53 per ounce, given that Aaron has 63 ounces of brand 856 iodine.
Let's assume x ounces of brand 213 iodine should be used.
So, the cost of brand 213 iodine would be 36 cents per ounce, which is $0.36/ounce.
The cost of brand 856 iodine is $1.58 per ounce.
To find the total cost of the mixture, we can multiply the cost per ounce of each brand by the number of ounces used:
Total Cost = (cost per ounce of brand 213) * (number of ounces of brand 213) + (cost per ounce of brand 856) * (number of ounces of brand 856)
Since the total cost is approximately $0.53 per ounce, we can set up the equation:
0.53 = (0.36/ounce) * x + (1.58/ounce) * 63
Now, let's solve the equation for x:
0.53 = 0.36x + 1.58(63)
0.53 = 0.36x + 99.54
0.36x = 0.53 - 99.54
0.36x = -99.01
x = (-99.01) / 0.36
By solving the equation, we find that x is approximately equal to -275.03 ounces. However, we cannot have a negative amount of iodine, so we need to choose the non-negative value.
Therefore, Aaron should use 0 ounces of brand 213 iodine to achieve a mixture that costs approximately $0.53 per ounce.
Please note that this solution assumes a linear relationship between the mixture's cost and the amounts of the two brands of iodine used.