!!!!!!!!!! 50 POINTS !!!!!!!!!!!! How would you go about solving this? Please provide formulae / explanation if needed, thank you.

To solve this problem, we can use the formula for calculating the mean (average) weight:

Mean = (Sum of weights) / (Number of parcels)

First, we know that the mean weight of all 7 parcels is 2.7 kg:

Mean = 2.7 kg

We also know that the mean weight of the remaining 4 parcels (after Larry delivers 3 parcels) is 3.3 kg:

Mean = 3.3 kg

We can set up equations using this information:

1. For the 7 parcels:
Mean = (Sum of weights of all 7 parcels) / 7

2. For the 4 parcels Larry didn't deliver:
3.3 kg = (Sum of weights of 4 parcels) / 4

We can solve these equations to find the total sum of weights for all 7 parcels and the sum of weights for the remaining 4 parcels.

Let's denote the weight of each of the 3 parcels Larry delivers as W kg.

So, for the 7 parcels, the total sum of weights is:
(2.7 kg) * 7 = 18.9 kg

For the 4 parcels Larry didn't deliver, the total sum of weights is:
(3.3 kg) * 4 = 13.2 kg

Since the total sum of weights for all 7 parcels is the sum of the weights of the 3 parcels Larry delivered and the 4 parcels he didn't deliver, we can write the equation:

18.9 kg = 3W + 13.2 kg

Now, solve for W:

18.9 kg - 13.2 kg = 3W

5.7 kg = 3W

W = 5.7 kg / 3

W = 1.9 kg

So, the weight of each of the 3 parcels Larry delivers is 1.9 kg.

semsee45 semsee45 · Answer 2 · 2024-03-26T12:01:19+01:00

Answer:

W = 1.9

Step-by-step explanation:

The mean is a measure of central tendency calculated by dividing the sum of a set of values by the total number of values.

[tex]\boxed{\rm Mean=\dfrac{\text{Sum of a set of values}}{\text{Total number of values}}}[/tex]

If Larry has a total of 7 parcels to deliver and the mean weight of the parcels is 2.7 kg, then the total weight of all the parcels is:

[tex]\rm Total\;weight=2.7 \; kg/parcel \times 7\;parcels\\\\ Total\;weight= \boxed{18.9\; \rm kg}[/tex]

If Larry delivers 3 of the parcels, and each of these parcels has a weight of W kg, then the total weight of the delivered parcels is:

[tex]\rm \text{Total weight of delivered parcels}=W\; kg/parcel \times 3\;parcels\\\\\text{Total weight of delivered parcels}=\boxed{3W\; \rm kg}[/tex]

If the mean weight of the other 4 parcels if 3.3 kg, then the total weight of the other 4 parcels is:

[tex]\rm \text{Total weight of other 4 parcels}=3.3\; kg/parcel \times 4\;parcels\\\\\text{Total weight of other 4 parcels}=\boxed{13.2\; \rm kg}[/tex]

To determine the value of W, set the sum of the delivered parcels and the other 4 parcels equal to the total weight of the parcels:

[tex]3W+13.2=18.9[/tex]

Solve for W:

[tex]3W+13.2-13.2=18.9-13.2\\\\\\3W=5.7\\\\\\\dfrac{3W}{3}=\dfrac{5.7}{3}\\\\\\W=1.9[/tex]

Therefore, the value of W is:

[tex]\Large\boxed{\boxed{W=1.9}}[/tex]