Question

If you could exactly afford either 2 units of x and 7 units of y, or 4 units of x and 3 units of y, then if you spent all of your income on y, how many units of y could you buy?

Answer 1

11 units of y

Explanation:

Let total income be I

We have the two equations

2x + 7y = I (1) (exactly afford 2 units of x and 7 units of y)

4x + 3y = I (2) (exactly afford 42 units of x and 3 units of y)

Multiply (1) by 2
==> 2(2x + 7y) = 2 x I

==> 4x + 14y = 2I (3)

Subtract (2) from (3)
(3) - (2)
==> 4x + 14y - (4x + 3y) = 2I - I

==> 4x + 14y - 4x - 3y = 2I
==> 14y - 3y = I (x terms cancel)

==> 11y = I

This represents an equation where if you buy 11 units of y, it will be your whole income

Answer: 11 units of y