1. At a basketball game, the ratio of the number of freshmen who attended to the number of juniors who attended was 3 to 4. The ratio of the number of juniors who attended to the number of seniors who attended was 7 to 6. What was the ratio of the number of freshmen to the number of seniors who attended?
-So its like 3:4 and 7:6 and do you add then or something? I am so confused, apparently the answer is 7 to 8?
2. Each of 3 boxes contains 18 pieces of candy. What is the least number of pieces of candy that can be moved from one box to another so that the box with the least number of pieces of candy contains 1/6 of the total number of pieces of candy?
-3:18-->1:6? Then 1:3? The answer key says 9... 6+3? I am pretty sure I am wrong haha
f:j = 3:4
j:s = 7:6
LCM(4,7) = 28, so
f:j = 21:28
j:s = 28:24
f:j:s = 21:28:24
so, f:s = 21:24 = 7:8
total candy = 54 pieces.
You want a box with only 9 pieces.
Each box has 18 pieces now.
So, just move 9 from one box to another.
1. To find the ratio of the number of freshmen to the number of seniors who attended the basketball game, we need to consider both given ratios.
First, let's express the ratio of freshmen to juniors as 3:4. This means that for every 3 freshmen, there are 4 juniors in attendance.
Next, we have the ratio of juniors to seniors, which is 7:6. This means that for every 7 juniors, there are 6 seniors in attendance.
To find the ratio between freshmen and seniors, we can combine these two ratios. Since both ratios involve juniors, we can consider juniors as a common factor and cancel it out.
To do this, we multiply the ratio of freshmen to juniors (3:4) with the ratio of juniors to seniors (7:6).
(3/4) * (7/6) = (3 * 7) / (4 * 6) = 21 / 24
Now, simplify the ratio by dividing both numbers by their greatest common divisor, which is 3 in this case:
21 / 24 = (21 ÷ 3) / (24 ÷ 3) = 7 / 8.
Therefore, the ratio of freshmen to seniors who attended the basketball game is 7 to 8.
2. In this problem, we want to find the minimum number of candy pieces that need to be moved from one box to another, such that the box with the fewest pieces contains 1/6 of the total number of pieces.
Each box initially contains 18 pieces of candy, so the total number of candy pieces is 3 * 18 = 54 pieces.
To determine how many pieces need to be moved, we'll first find what 1/6 of the total number of pieces is:
(1/6) * 54 = 9.
So, the box with the fewest pieces should contain 9 pieces, which means we need to move from the other boxes to achieve this.
Since we want to equalize the number of pieces in each box, we need to distribute the excess to the box with the fewest pieces.
Since each box initially contains 18 pieces, and the target number is 9, we need to move (18 - 9) = 9 pieces from each of the other two boxes to one of the boxes.
Therefore, the least number of pieces of candy that needs to be moved is 9.