A 45 inch string is cut into 2 pieces. If the ratio of the longer piece to the shorter piece is 3:2, what is the length of the shorter piece?
Since there is a ratio of 3:2, there must be five equal parts in the whole... 45/(3+2)=9 So each part is equal to 9 inches. So the shorter piece is 2(9)=18 inches.
So we know that two pieces should equal 45 inches. It says that the ratio of the longer piece to the shorter piece is 3:2, which means that when multiplying 3/2 with the shorter piece, you should get the length of the longer piece. Since I don't know the formula, you might if you have learnt this already, I will use the substitution method. So I can try the number 10. If I do 10*3/2, I get 15. 10+15 is not equal to 45, so its too low. Now I will try 15. 15*3/2 is 22.5, and that cannot be the answer, because it is half of the full answer, so there won't be a larger or shorter one. Now I tried 20. This gives me 30. That is too big. So I can tell my answer will be in between 15 and 20. Now I tried 18. When I try 18, when multiplying with 3/2, I get 27. 27 + 18 = 45. Therefore we can conclude the longer side is 27 inches and the shorter side is 18 inches. Hope this helps! :D