### Instruction: George purchases a sack of apples, a bunch of bananas, a cantaloupe, and a carton of dates for $ \$ 20$. If a carton of dates costs twice as much as a sack of apples and the price of a cantaloupe is equal to the price of a sack of apples minus a bunch of bananas, how much would it cost George to purchase a bunch of bananas and a cantaloupe?### Response: I need to find the price of a bunch of bananas and a cantaloupe in terms of the other prices.
Let me use some variables to represent the prices: $a$ for apples, $b$ for bananas, $c$ for cantaloupe, and $d$ for dates.
The problem gives me some relationships between these variables: $d = 2a$, $c = a - b$, and $a + b + c + d = 20$.
I want to find $b + c$, so I need to eliminate $a$ and $d$ from the equations.
I can use the first equation to substitute $d$ with $2a$ in the third equation: $a + b + c + 2a = 20$.
Simplifying, I get $3a + b + c = 20$.
I can use the second equation to substitute $c$ with $a - b$ in this equation: $3a + b + a - b = 20$.
Simplifying, I get $4a = 20$.
Solving for $a$, I get $a = 5$.
Now I can plug this value into the second equation to find $c$: $c = a - b = 5 - b$.