Question

If a person can spend at most $20 on x apples and y bananas, where each banana costs twice as much as an apple, which inequality represents this situation?

Answer 1

Let the cost of one apple be denoted as \( a \). Then, the cost of one banana, since it is twice as expensive as an apple, will be \( 2a \).

If the person buys \( x \) apples and \( y \) bananas, the total cost can be expressed as:

\[
\text{Total Cost} = (cost \, of \, apples) + (cost \, of \, bananas) = ax + 2ay
\]

We know that the person can spend at most $20, which gives us the inequality:

\[
ax + 2ay \leq 20
\]

This inequality represents the situation described. You can also factor out \( a \) (if \( a > 0 \)) to simplify it, resulting in:

\[
a(x + 2y) \leq 20
\]

However, the initial form \( ax + 2ay \leq 20 \) accurately captures the conditions of the problem, considering \( a \), \( x \), and \( y \) are all non-negative.