In the economy of Mungo there is a person called Ike. Ike has a red income of 40 and a blue income of 10. 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 pay twice 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

(b) he consumes at least 5 units of ambrosia.

Explanation:

Ike has a red income of 40 and a blue income of 10

Step 1

1 blue income = 1bcu

1 red income = 1 rcu

1 unit of ambrosia = 1 bcu

1 unit of ambrosia = 2 rcu

1 unit of bubblegum = 1 bcu

1 unit of bubblegum = 6 rcu

Step 2

You have to pay twice for what you buy, once in red currency, once in blue currency.

1 unit of ambrosia = 1 bcu * 2 = 2bcu

1 unit of bubblegum = 1 bcu * 2 = 2bcu

1 unit of ambrosia = 2 rcu * 2 = 4 rcu

1 unit of bubblegum = 6 rcu * 2 = 12 rcu

Step 3

For blue currency

When Ike buys 1 unit of ambrosia (2bcu) and 1 unit of bubblegum (2bcu) he is left with 10bcu -(2bcu+2bcu) = 6bcu

For red currency

When Ike buys 1 unit of ambrosia (4rcu) and 1 unit of bubblegum (12 rcu) he is left with 40 rcu -(4 rcu + 12rcu) = 24 rcu

Step 4

For blue currency

When Ike buys 1 unit of ambrosia (2bcu) and 1 unit of bubblegum (2bcu) he is left with 6bcu -(2bcu+2bcu) = 2bcu

For red currency

When Ike buys 1 unit of ambrosia (4rcu) and 1 unit of bubblegum (12 rcu) he is left with 24 rcu -(4 rcu + 12rcu) = 8 rcu

Step 5

For blue currency

When Ike buys 1 unit of ambrosia (2bcu) he is left with 2bcu - 2bcu = 0bcu. (All blue income spent)

For red currency

When Ike buys 1 unit of ambrosia (4rcu) he is left with  8rcu -4 rcu = 4 rcu

Ike purchased a total of 6 units of ambrosia and spent all of his blue income with 4 red income left.

The answer is therefore B  which means he consumes at least 5 units of ambrosia.

c.

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