4(b - 6) + 19 # Starting equation
4b - 24 + 19 # Using the distributive property
4b - 5 # Simplified expression
To start you would turn 4 2/3 into a mixed number by multiplying 4 and 3 and adding 2. Your mixed number would be 14/3. Then, you want to find how many 2/3 yard long pieces of string will fit into 14/3 so you devid 14/3 by 2/3 and you get 7. So 7 2/3 yard pieces of string will fit into 4 2/3.
To check your work you can multiply 2/3 by 7 and you will get 4 2/3.
Answer:
5 sets
Step-by-step explanation:
The average number of pieces per set is the ratio of the total number of pieces to the total number of sets.
Let x represent the number of 3-piece sets. Then the total number of pieces is ...
3x +5(5) +10(2) = 3x +45
The total number of sets is ...
x +5 +2 = x +7
We want the ratio of these numbers to be 5 pieces per set:
(3x +45)/(x +7) = 5
3x +45 = 5x +35 . . . . . multiply by (x+7)
10 = 2x . . . . . . . . . . subtract (3x+35)
5 = x . . . . . . . . . divide by 2
Divya owns 5 sets with 3 pieces.
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<em>Alternate solution</em>
Each 10-piece set has 5 more pieces than average, so the two of them total 10 more pieces than average.
Each 3-piece set has 2 fewer pieces than average. The total number of 3-piece sets must have a total of 10 fewer pieces than average in order to balance the excess of the 10-piece sets. That is, there must be 10/2 = 5 of the 3-piece sets to have a total lof 10 fewer pieces than average.
Altogether, the differences from average must total zero.
This question is incomplete no ocitures
