Dan gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet. He picks 3 times as many cola bottles as smarties. He also picks twice as many marshmallows as smarties. What proportion of the bag of sweets are smarties?
Give your answer in its simplest form.
1
To solve this problem, let's use variables:
- Let's call the number of smarties Dan picks "S".
- Dan picks 3 times as many cola bottles as smarties, so he picks 3S cola bottles.
- Dan picks twice as many marshmallows as smarties, so he picks 2S marshmallows.
The total number of sweets in Dan's bag is S + 3S + 2S = 6S.
The proportion of the bag that is smarties is S/6S, which simplifies to 1/6.
Therefore, the answer is:
Dan's bag of sweets includes smarties in a proportion of 1/6.
To find the proportion of smarties in the bag of sweets, we need to compare the number of smarties to the total number of sweets.
Let's assume the number of smarties Dan picks is "x".
According to the information given in the question:
- He picks three times as many cola bottles as smarties, so the number of cola bottles he picks is 3x.
- He also picks twice as many marshmallows as smarties, so the number of marshmallows he picks is 2x.
Therefore, the total number of sweets in the bag is the sum of the number of smarties, cola bottles, and marshmallows:
Total = x + 3x + 2x = 6x
Now we can calculate the proportion of smarties in the bag. By dividing the number of smarties by the total number of sweets, we get:
Proportion of smarties = x / (x + 3x + 2x) = x / 6x
The x term cancels out, and we are left with:
Proportion of smarties = 1 / 6
Therefore, the proportion of smarties in the bag of sweets is 1/6 or 1:6.
3+2+1 = 6
so, 1/6