Directions: Analyze the data presented in the table below to answer the question.

The following table displays the total volume of smart wearables (Smartwatches and Fitness bands) shipped by five different electronics brands, alongside the ratio of Smartwatches to Fitness bands shipped by each brand.

Brands	Total smart wearables shipped	Smartwatches : Fitness bands
P	700	5:9
Q	850	9:8
R	980	4:3
S	1200	8:7
T	1020	5:7

Determine the total number of fitness bands shipped by all five brands combined.

The correct answer is 2425.

Step-by-Step Explanation:

To determine the total number of fitness bands shipped by all five brands combined, we need to calculate the number of fitness bands shipped by each brand individually using the total volume and the ratio of Smartwatches to Fitness bands.

For any brand with a Smartwatches to Fitness bands ratio of $a:b$, the fraction representing Fitness bands out of the total wearables is given by:

$\text{Fraction of Fitness bands}=\frac{b}{a+b}$

1. Brand P:
Total wearables = 700
Ratio (Smartwatches : Fitness bands) = 5 : 9
Sum of ratio terms = 5 + 9 = 14

$\text{Fitness bands (P)}=700\times \frac{9}{14}=50\times 9=450$

2. Brand Q:
Total wearables = 850
Ratio (Smartwatches : Fitness bands) = 9 : 8
Sum of ratio terms = 9 + 8 = 17

$\text{Fitness bands (Q)}=850\times \frac{8}{17}=50\times 8=400$

3. Brand R:
Total wearables = 980
Ratio (Smartwatches : Fitness bands) = 4 : 3
Sum of ratio terms = 4 + 3 = 7

$\text{Fitness bands (R)}=980\times \frac{3}{7}=140\times 3=420$

4. Brand S:
Total wearables = 1200
Ratio (Smartwatches : Fitness bands) = 8 : 7
Sum of ratio terms = 8 + 7 = 15

$\text{Fitness bands (S)}=1200\times \frac{7}{15}=80\times 7=560$

5. Brand T:
Total wearables = 1020
Ratio (Smartwatches : Fitness bands) = 5 : 7
Sum of ratio terms = 5 + 7 = 12

$\text{Fitness bands (T)}=1020\times \frac{7}{12}=85\times 7=595$

Total Fitness Bands Shipped by All Brands Combined:

$\text{Total}=450+400+420+560+595=2425$

Thus, the total number of fitness bands shipped by all five brands combined is 2425.