for word problem experts

Question

4/7 of birthday cake was eaten on your birthday. The next day dad ate 1/2 of what was left. You get to finish the cake how much is left

in my book

let x be cake

so 4/7 cake has been eaten means 4x/7

x-4x/7 =3x/7

now 3x/7*1/2

answer come 3/14

 

 

my confusion is

4/7 of cake means 4/7 is part of cake so we took 4x/7

now when dad ate 1/2 part of remaining cake so it should like x/2 but when i trying to solve this answer come 3x^2/14. 

So for only first sentence we took 4x/7 and second sentence took 1/2. Why this imbalance both are cake parts

therefore how we know when to use x

 

please sent me detail information 

 

 

Answer 1

Don't know why they said "let x be cake." The cake is a known quantity (1 whole cake, not a variable...)

 

Start with 1, not x.

 

4/7 is eaten at first, so 3/7 are left.

 

It's hard to cut 3/7 in half, so you think of it as 6/14.

 

Dad eats 3 of those 14ths, so there are 3 more 14ths left.

 

Done.

Answer 2

Your answer of 3/14 is correct.

 

You could probably leave "x" out of this, as it is part of the confusion, but it can be solved either way. Your point of confusion is where you reference the remaining cake portion as x/2, which means half of the entire cake, rather than half of the portion that is left after 4/7ths was consumed.

 

If the entire cake is x, then the remaining cake after 4/7ths is consumed is:

 

x * (1 - 4/7) = 3x/7 (or just 1 - 4/7 = 3/7)

 

So, when dad eats half of the remaining cake, he is consuming not 1/2 of x, but:

 

1/2 * [3x/7] = 3x/14 (or just 1/2 * 3/7 = 3/14)

 

You can probably take it from there....

 

Make sense?