Alan has 150 sweets. The ratio of Alan's sweets to Ben's sweets is 3 : 5.How many sweets do they have altogether?
Question
Alan has 150 sweets. The ratio of Alan's sweets to Ben's sweets is 3 : 5.How many sweets do they have altogether?
Solution
To solve this problem, we need to understand that the ratio given represents the distribution of sweets between Alan and Ben.
Step 1: Identify the ratio The ratio of Alan's sweets to Ben's sweets is 3:5. This means that for every 3 sweets Alan has, Ben has 5.
Step 2: Determine the total parts in the ratio The total parts in the ratio are 3 (Alan's part) + 5 (Ben's part) = 8 parts.
Step 3: Determine the value of each part We know that Alan has 150 sweets, which represents 3 parts of the ratio. Therefore, each part is worth 150 sweets / 3 = 50 sweets.
Step 4: Determine the number of sweets Ben has Ben has 5 parts of the ratio, so he has 5 parts * 50 sweets/part = 250 sweets.
Step 5: Determine the total number of sweets The total number of sweets they have together is 150 sweets (Alan) + 250 sweets (Ben) = 400 sweets.
So, Alan and Ben have 400 sweets altogether.
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