The farmer sells a 41.9915-tonne load to a buyer who takes a
single scoop of tomatoes from a random spot in the load.
If the sample has approximately 300 tomatoes and 92% are acceptable,
how much is the load worth? Tomatoes sell for $94.40 per tonne.
Well, let's do some math here. If the sample has 300 tomatoes and 92% of them are acceptable, that means 92% of 300 tomatoes are acceptable.
So, 92% of 300 tomatoes is 276 tomatoes. That's a lot of tasty tomatoes!
Now, if the load weighs 41.9915 tonnes and tomatoes sell for $94.40 per tonne, we can calculate the worth of the load by multiplying the weight of the load by the price per tonne.
So, the load is worth 41.9915 tonnes * $94.40 per tonne.
But wait! We need to take into account that only 92% of the tomatoes are acceptable. So, we can multiply the total value by 92% to find the final worth of the load.
To summarize, the load is worth 41.9915 tonnes * $94.40 per tonne * 92%.
Now, let's grab our calculators and find out the answer!
To calculate the value of the load, we need to determine the weight of the load that is acceptable.
If the sample has approximately 300 tomatoes and 92% of them are acceptable, we can calculate the weight of acceptable tomatoes in the sample as follows:
Weight of acceptable tomatoes in the sample = (Weight of sample) x (Percentage of acceptable tomatoes)
= (300 tomatoes) x (0.92)
Now we have to determine the weight of the entire load.
Weight of entire load = (Weight of sample) / (Percentage of sample from the load)
= (Weight of sample) / (1 / Total load)
Given that the weight of the sample is 41.9915 tonnes, we can calculate the weight of the entire load as follows:
Weight of entire load = 41.9915 tonnes / (1 / Total load)
To determine the value of the load, we multiply the weight of the entire load by the price per tonne:
Value of the load = (Weight of entire load) x (Price per tonne)
Given that the price per tonne is $94.40, we can calculate the value of the load as follows:
Value of the load = (Weight of entire load) x ($94.40)
Let's calculate the value of the load step-by-step:
Weight of acceptable tomatoes in the sample = (300 tomatoes) x (0.92)
= 276 tomatoes
Weight of entire load = 41.9915 tonnes / (1 / Total load)
Since we don't have the information about the percentage of the sample from the load, we cannot calculate the weight of the entire load and hence the value of the load.
To find the value of the load, we need to determine the weight of the acceptable tomatoes in the load.
First, we can calculate the total number of acceptable tomatoes in the load. Since 92% of the tomatoes are acceptable, we can multiply the total number of tomatoes in the sample (300) by 0.92:
300 tomatoes * 0.92 = 276 acceptable tomatoes
Next, we need to find the weight of each tomato. To do this, we divide the weight of the load (41.9915 tonnes) by the number of tomatoes in the load:
Weight of each tomato = 41.9915 tonnes / 276 tomatoes
Now, we can determine the weight of the acceptable tomatoes in the load by multiplying the weight of each tomato by the total number of acceptable tomatoes:
Weight of acceptable tomatoes = Weight of each tomato * Total number of acceptable tomatoes
Finally, to find the value of the load, we multiply the weight of the acceptable tomatoes by the price per tonne:
Value of the load = Weight of acceptable tomatoes * Price per tonne
Let's calculate it:
Weight of each tomato = 41.9915 tonnes / 276 tomatoes
Weight of each tomato ≈ 0.1522 tonnes (approx.)
Weight of acceptable tomatoes = 0.1522 tonnes/tomato * 276 tomatoes
Weight of acceptable tomatoes ≈ 41.9923 tonnes (approx.)
Value of the load = 41.9923 tonnes * $94.40/tonne
Value of the load ≈ $3,963.82
Therefore, the load is worth approximately $3,963.82.