Four puzzles that were manufactured contained a total of 420 pieces. The next 6 puzzles contained a total of 630 pieces. If the relationship between the number of puzzles and the total number of puzzle pieces continues to be proportional, which could be the missing entries in the table?

Complete Question:

Four puzzles that were manufactured contained a total of 420 pieces. The next 6 puzzles contained a total of 630 pieces. If the relationship between the number of puzzles and the total number of puzzle pieces continues to be proportional, which could be the missing entries in the table?

A.) 8 puzzles 800 pieces

B.) 8 puzzles 840 pieces

C.) 10 puzzles 1000 pieces

D.) 10 puzzles 1200 pieces

B

Step-by-step explanation:

Given the table:

Number of puzzles (x) - - - - Number of pieces (y)

4 - - - - - - - - - - - - - - - - - - - - - - - - - - 420

6 - - - - - - - - - - - - - - - - - - - - - - - - - - 630

Calculating the relationship between number puzzles (x) and number of pieces (y)

x = ky

Where k = proportionality constant

> 4 = k420 ; k = 420/4 = 105

> 6 = k630 ; k = 630/4 =! 105

Therefore assuming the total number of puzzles and puzzle pieces remains horizontal.

Taking A

8 = k800 ; k = 800/8 = 100

Taking B

8 = k840 ; k = 840/8 = 105

Taking C

10 = k1000; k = 1000/ 10 = 100

Taking D

10 = k1200; k = 1200/ 10 = 120

Therefore only ption B maintains the 105 L - value