Question

In how many different ways can five cent and eight cent stamps be used to make $2.43? In process, show the different combinations of stamps that make $2.43. In solution, tell how many ways you found.
Pls help me pls.

Answer 1

since 5+8 = 13, one obvious combination is

2.35 in 5-cent stamps, and one 8-cent stamp
Since 5*8=40, decreasing the 5-cent count by 8 and increasing the 8-cent count by 5 will keep the total at 2.43

So, just build a table

5¢ 8¢
47 1
39 6
...
7 26

Answer 2

thank u so much steve

Answer 3

15

Answer 4

number of 5s = 7 number of 8s = 26 check 243
number of 5s = 15 number of 8s = 21 check 243
number of 5s = 23 number of 8s = 16 check 243
number of 5s = 31 number of 8s = 11 check 243
number of 5s = 39 number of 8s = 6 check 243
number of 5s = 47 number of 8s = 1 check 243
Total combinations that match 6 for 243 using 5s and 8s

number of 5s = 6 number of 8s = 57 check 486
number of 5s = 14 number of 8s = 52 check 486
number of 5s = 22 number of 8s = 47 check 486
number of 5s = 30 number of 8s = 42 check 486
number of 5s = 38 number of 8s = 37 check 486
number of 5s = 46 number of 8s = 32 check 486
number of 5s = 54 number of 8s = 27 check 486
number of 5s = 62 number of 8s = 22 check 486
number of 5s = 70 number of 8s = 17 check 486
number of 5s = 78 number of 8s = 12 check 486
number of 5s = 86 number of 8s = 7 check 486
number of 5s = 94 number of 8s = 2 check 486
Total combinations that match 12 for 486 using 5s and 8s

number of 5s = 5 number of 8s = 11 check 113
number of 5s = 13 number of 8s = 6 check 113
number of 5s = 21 number of 8s = 1 check 113
Total combinations that match 3 for 113 using 5s and 8s

public class Pow17Part2AndPart3 {
public static void main (final String... args) throws Exception {
findTotalCombinations(243);
findTotalCombinations(486);
/* Part 3.
* How many stamp combinations of 0.5 and 0.8 is in $1.13
* */
findTotalCombinations(113);
}
/* To make the technique resusable we create a function so we can vary
the total we are trying to find.
*/
private static void findTotalCombinations(int valueToFindCombinationsOf) {
/* Compare a matrix of possibilities against the expected outcome. */
int totalCombinationThatMatch = 0;

/* Iterate through total number of 5s that can be in 243. */
for (int num5 = 0; num5 < (valueToFindCombinationsOf / 5) +1 ; num5++) {
/* Calculate the total value of the five cent stamp for this iteration. */
int fiveTotal = num5 * 5;
/* Iterate through total number of 8s that can be in 243. */
for (int num8 = 0; num8 < (valueToFindCombinationsOf / 8) +1; num8++) {
/* Calculate the total value of the eight cent stamp for this iteration. */
int eightTotal = num8 * 8;
/* See if the current value of 8 cent stamps plus the five stamps
are equal to 243.
*/
if (eightTotal + fiveTotal == valueToFindCombinationsOf) {
/* Output the results if the total is 243. */
System.out.printf("number of 5s = %d \t number of 8s = %d " +
"\t check %d \n", num5, num8,
num5 * 5 + num8 * 8);
totalCombinationThatMatch++;
}
}
}
System.out.printf("Total combinations that match %d for %d using 5s and 8s \n",
totalCombinationThatMatch,
valueToFindCombinationsOf);
System.out.println();
}
}