A bowl contains 675 sweets which are coloured either red, blue or green.
The ratio of red sweets to blue sweets is 3 : 7
The ratio of blue sweets to green sweets is 4 : 5
Calculate the number of blue sweets that are in the bowl.
please provide an explanation; i would like to understand for future ref :)
nevermind! i got the answer: 252
b = (4/5) g , so g = (5/4) b
r = (3/7) b
so
(3/7) b + (5/4) b + b = 675
(12/28) b + (35/28) b + (28/28) b = 675
(75/28) b = 675
b = 252 , sure enough :)
that is incorrect
To find the number of blue sweets in the bowl, we need to follow a step-by-step approach based on the given information:
Step 1: Set up the ratios
The ratio of red sweets to blue sweets is given as 3:7.
The ratio of blue sweets to green sweets is given as 4:5.
Step 2: Find the common ratio
Since the blue sweets appear in both ratios, we can find a common ratio to relate them. To do this, we compare the blue sweets in both ratios, resulting in a new ratio of 7:4.
Step 3: Determine the scale factor
To find the scale factor, we need to add the terms in the ratio. The scale factor is the sum of 7 and 4, which is 11.
Step 4: Calculate the number of blue sweets
Now that we have the scale factor, we can calculate the number of blue sweets. Since there are 675 sweets in total, we can express the number of blue sweets using the ratio: 7/11 * 675 = 7 * (675/11) = 7 * 61.36 ≈ 429.5.
However, it is essential to note that the number of sweets must be a whole number. Therefore, we round the result to the nearest whole number.
Therefore, the number of blue sweets in the bowl is approximately 430.
By following these steps, you can understand how to solve similar problems in the future by setting up ratios, finding a common ratio, determining the scale factor, and calculating the required number based on the given information.