Sophina brought 3 yards of trim to put around a rectangular scarf. She does not want the scarf to be wider than 12 inches or narrower than 6 inches. Using whole numbers, if she uses all the trim, what are the possible dimensions of her scarf in inches?
Answer (3)
3 yards equal 108 inches you can split it in half and get 54 then see how many 12 go in to it and that would be 4 and there would be 6 left over. then we have 54 and see how many 6 can go into it then add 6 more then that would equal 10 6 so that means we would have four twelths and ten sixths
Sophina's scarf dimensions, using all 3 yards of trim, can be: 6x48, 7x47, 8x46, 9x45, 10x44, 11x43, or 12x42 inches, respecting width constraints.
Let's denote the width of the scarf as w inches and the length as l inches. The perimeter of the scarf would be 2w + 2l , and since Sophina uses all 3 yards of trim (which is 9 feet or 108 inches), we have:
2 w + 2 l = 108
Given that the scarf's width must be between 6 and 12 inches, we have the inequality:
6 ≤ w ≤ 12
Now, we can solve for possible dimensions by substituting different values of w within this range and finding the corresponding l values:
For w = 6 , l = 2 108 − 2 × 6 = 48 inches.
For w = 7 , l = 2 108 − 2 × 7 = 47 inches.
For w = 8 , l = 2 108 − 2 × 8 = 46 inches.
For w = 9, l = 2 108 − 2 × 9 = 45 inches.
For w = 10, l = 2 108 − 2 × 10 = 44 inches.
For w = 11 , l = 2 108 − 2 × 11 = 43 inches.
For w = 12, l = 2 108 − 2 × 12 = 42 inches.
So, the possible dimensions of Sophina's scarf (in inches) are:
6 × 48
7 × 47
8 × 46
9 × 45
10 × 44
11 × 43
12 × 42
Sophina can make her scarf with various dimensions using 3 yards of trim (108 inches total). Possible width and length combinations, according to her width restrictions (6-12 inches), are from 6x48 up to 12x42 inches. The valid dimensions include pairs like 6×48, 7×47, up to 12×42 inches.
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