Question

Ann, Ben, and Cindy were eating Skittles. The ratio of the numbers of candies they ate is 5:5:7. If Cindy ate 30 Skittles less than Ann and Ben together, what is the total number of Skittles the three of them ate?

Answer 1

170 skittles. 50 eaten by Ann, 50 eaten by Ben and 70 eaten by Cindy.

Explanation:

First, what we must do, is establish a constant of proportion, which is a variable we'll place along with the ratio of Skittles eaten by the three, which would be the proportional quantities of this problem. Let our constant be "s".

1. Assuming that the names and the ratio are respective (meaning that Ann = 5, Ben = 5 and Cindy = 7), we establish our numbers/variables:

5s + 5s = 10s (10s would be the number of Skittles Ann and Ben ate together).

10s - 7s = 3s (3s number of Skittles Cindy ate less than Ann and Ben together).

2. We know how many Skittles Cindy ate less than Anna and Ben together, and that is 30 skittles. That means that the numbers in the ratio (5, 5, and 7), multiplied by 10, give us the actual number of Skittles the 3 people ate.

2.1 We know this, because if 3s corresponds to the number of Skittles Cindy ate less that Anna and Ben together, and we know that that number is actually 30, we just divide 30 into 3:

30 / 3 = 10

3. Now, we just do what we discovered above:

5 * 10 = 50

5 * 10 = 50

7 * 10 = 70

50 + 50 + 70 = 170

Hope it helped,

BiologiaMagister

Answer 2

170 skittles

Explanation:

Given that there are certain number of Skittles. And they were shared by Ann, Ben and Cindy.

The ratio in which they shared is 5:5:7

Let k be the constant of proportion.

Then Ann ate 5k skittles, Ben 5k and cindy 7k skittles

Sum of skittles Ann and Ben ate = 5k+5k =10k

Less: Cindy ate = 7k

No of skittles cindy ate less = 3k

But 3k = 30 (given)

Hence k =10

Total no of skittles all three ate = 5k+5k+7k = 17k = 17(10) = 170