A very old vending machine accepts only nickels (n) and dimes (d). Candy costs up to $0.50, but sometimes the machine will dispense candy without any coins being inserted into the machine. Which inequality shows all of the ways to obtain a candy bar from the machine?
how about
5n + 10d ≤ 50
n + 2d ≤ 10 , where n and d are whole numbers
To determine the possible ways to obtain a candy bar from the vending machine, we need to consider the combinations of nickels (n) and dimes (d) that add up to a value less than or equal to $0.50.
Let's break down the problem:
1. The value of a nickel is $0.05 (5 cents).
2. The value of a dime is $0.10 (10 cents).
3. The maximum cost of a candy bar is $0.50 (50 cents).
We can define the number of nickels as 'n' and the number of dimes as 'd'. The total value of nickels and dimes can be represented as:
Total value = (Value of nickels * number of nickels) + (Value of dimes * number of dimes)
To obtain a candy bar, the total value should be less than or equal to $0.50. Therefore, the inequality to represent this condition would be:
(0.05 * n) + (0.10 * d) ≤ 0.50
This inequality shows all the possible ways to obtain a candy bar from the vending machine by using nickels and dimes, as it ensures the total value is within the cost range of the candy bar.