Hi I have a maths problem I can't figure out please someone help.
Zac had some 2c stamps and 5c stamps.he needed to put 30c on a postcard to mail it.what combinations of stamps could he use.
Assuming we can pay using either all 2c or 5c stamps...
let's start with
0 2c ----> 6 5c
1 2c ----> leaves 28 c, can't be done with 5c's
..
5 2c ---> leaves 20 c, paid with 4 5c
..
10 2c ---> 2 5c
15 2c ---> 0 5c
so in the form (2c , 5c) we have
(0,6) , (5,4), (10,2), and (15,0)
To solve this problem, we need to find all possible combinations of 2c and 5c stamps that add up to 30c. Here's how you can approach it:
1. Begin by listing the possible quantities of 2c stamps that Zac could use, starting from zero and incrementing by one until the largest quantity that would still allow the sum to be less than or equal to 30c.
- 0 2c stamps
- 1 2c stamp
- 2 2c stamps
- 3 2c stamps
- ...
2. For each quantity of 2c stamps, calculate the sum of the value of those stamps and check if the sum is less than or equal to 30c.
- For 0 2c stamps, the sum is 0c. Since 0c is less than 30c, it is a valid option.
- For 1 2c stamp, the sum is 2c. Since 2c is less than 30c, it is a valid option.
- For 2 2c stamps, the sum is 4c. Since 4c is less than 30c, it is a valid option.
- For 3 2c stamps, the sum is 6c. Since 6c is less than 30c, it is a valid option.
- ...
3. For each valid quantity of 2c stamps, calculate the remaining value needed for a total of 30c. This is done by subtracting the sum of 2c stamps from 30c.
- For 0 2c stamps, we need 30c - 0c = 30c more.
- For 1 2c stamp, we need 30c - 2c = 28c more.
- For 2 2c stamps, we need 30c - 4c = 26c more.
- For 3 2c stamps, we need 30c - 6c = 24c more.
- ...
4. With the remaining values, check if they are divisible by 5, as this would mean Zac can use some whole number of 5c stamps to complete the combination.
- For 0 2c stamps and requiring 30c more, 30c % 5 = 0, so Zac can use only 5c stamps to reach 30c.
- For 1 2c stamp and requiring 28c more, 28c % 5 = 3, so there is no combination possible using this quantity of 2c stamps.
- For 2 2c stamps and requiring 26c more, 26c % 5 = 1, so there is no combination possible using this quantity of 2c stamps.
- For 3 2c stamps and requiring 24c more, 24c % 5 = 4, so there is no combination possible using this quantity of 2c stamps.
- ...
By following this process, you can continue listing the combinations and identifying if they are possible or not. In this case, there will be only one valid combination: using only 5c stamps to reach a total of 30c.