Question

A cake is cut into 3 pieces whose weights are in the ratio 2:1:4. If the third piece weighs 360 g more than the second, how much did the whole cake weigh?

Answer 1

We know that the pieces are in a 2:1:4 ratio and that the third piece is 360 grams more than the second piece.

Let's write the values ​​of the pieces below:

2:1:4 = 2x        1x        4x

The second piece is just X (or 1x)

The third piece is the same value of second piece + 360g (4x grams)

We have to calculate the weight difference between these two:

4x - x = 3x

3x = 360 (We found the added weight)

Now we have to divide this value by the number of pieces to find de X value

X = 360 / 3 = 120

X = 120

Let's remember the proportion of the pieces of the cake: 2:1:4

first piece: 2x = 2*120 = 240g

second piece: x = 1*120 = 120g

third piece: 4x = 4*120 = 480g

Whole cake weigh: 240 + 120 + 480 = 840g

The whole cake weigh is 840 grams///