Ellie has three colored ribbons, red, blue and green with lengths 70 cm, 84 cm and 105 cm respectively. She decides to make a set by cutting these three ribbons into smaller pieces of equal lengths with no leftovers. (a) Find the greatest possible length that she can cut from each of these ribbons. (b) Find how many sets can she make altogether.
Answers
Given :- Ellie has three colored ribbons, red, blue and green with lengths 70 cm, 84 cm and 105 cm respectively. She decides to make a set by cutting these three ribbons into smaller pieces of equal lengths with no leftovers .
To Find :-
(a) Find the greatest possible length that she can cut from each of these ribbons.
(b) Find how many sets can she make altogether.
Answer :-
In order to find the greatest possible length cut from each ribbons , we need to find HCF of length of ribbons.
so, Prime factors of 70 cm, 84 cm and 105 cm is
→ 70 = 2 * 5 * 7
→ 84 = 2 * 2 * 3 * 7
→ 105 = 5 * 3 * 7
then
→ HCF = 7 .
therefore, greatest possible length of ribbon cuts from each is 7 cm .
now,
→ Total sets from first ribbon = 70/7 = 10 sets .
→ Total sets from first ribbon = 84/7 = 12 sets .
→ Total sets from first ribbon = 105/7 = 15 sets .
hence,
→ Total sets she can make altogether = 10 + 12 + 15 = 37 sets.
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