2.41 In the economy of Mungo, discussed in your workbook, there is a third perso

Question

2.41 In the economy of Mungo, discussed in your workbook, there is a third person called Ike. Ike has a red income of 40 and a blue income of 10. (Recall that blue prices are 1 bcu [blue currency unit] per unit of ambrosia and 1 bcu per unit of bubblegum. Red prices are 2 rcus [red currency units] per unit of ambrosia and 6 rcus per unit of bubblegum. You have to paytwice for what you buy, once in red currency, once in blue currency.) If Ike spends all of his blue income, but not all of his red income, then it must be that:
(a) he consumes at least 5 units of bubblegum.
(b) he consumes at least 5 units of ambrosia.
(c) he consumes exactly twice as much bubblegum as ambrosia.
(d) he consumes at least 14 units of bubblegum.
(e) he consumes equal amounts of ambrosia and bubblegum.

answer is b..please show me full working

Explanation / Answer

Ike had Red income 40 and blue income 10

Now according to given question

1 blue income = 1bcu

and 1bcu=1 ambresia

1 bcu = 1 bubblegum

1 red income = 1 rcu

and 2 rcu = 1 ambresia

6 rcu = 1 bubblegum

now he said he had to pay twice for what he purchased so

2 bcu = 1 ambrosia and 2 bcu = 1 bubblegum

4 rcu = 1 ambresia and 12 rcu = 1 bubblegum

now another condition is he had to spend once in red currency and once in blue currency

so

first round

spend blue currency and buy 1 ambrosia with 2 bcu and left with 8 bcu then ike puchased 1 bubblegum with 2 bcu and left with 6 bcu

spend red currency ike buy 1 ambrosia with 4 rcu and left with 36 rcu then ike buy 1 bubblegum for 12 rcu and left with 24 rcu

second round

blue currency ike buy 1 ambrosia with 2 bcu and left with 6 bcu and buy 1 bubblegum for 2 bcu and left with 4 bcu

red currency ike buy 1 ambrosia with 4rcu and left with 20 rcu and buy 1 bubblegum for 12 rcu and left with 8 rcu

third round

blue currency ike buy 1 ambrosia for 2 bcu and left with 2 bcu only from which ike purchased 1 bubble gum and no blue currency is left

red currency ike buy 1 ambrosia for 4 rcu and left with only 4 rcu through which she cannot purchase any more bubblegum

Hence Ike puchased total of 5 ambrosia and 4 bubblegum and she is left with zero blue currency and 4 red currency

That's why answer will be B that  he consumes at least 5 units of ambrosia.

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