What is the minimum number of candy pieces that alan has if there are at least 47 pieces of candy among both noah and alan

33

Step-by-step explanation:

Let's just give things vaiables and see how it goes.  let's call the number of candy pieces Alan has A and the ones Noah has N.  now, it tells us A = 5 + 2N, five more than twice Noah's.  it also tells us that A + N is at least 47.  or in other words A + N ≥ 47

Well, we know what A is in terms of N so let's use that instead.

A + N ≥ 47

5 + 2N + N ≥ 47

Now let's solve with algebra.

5 + 2N + N ≥ 47

5 + 3N ≥ 47

3N ≥ 47 - 5

3N ≥ 42

N ≥ 14

Then going back to Alan's candy let's plug 14 in for N, because we know that Noah has to have at least 14

A + N ≥ 47

A + 14 ≥ 47

A ≥ 33

So that tells us Alan must have at least 33.  If there's something you didn't get don't hesitate to ask.