Suppose that a store offers gift certificates in denominatio

Suppose that a store offers gift certificates in denominations of $25 and $40. Determine the possible total amounts you can form using these gift certificates. Proof your answer using strong mathematical induction.

Solution

Here different denominations of 25 and 40 can be given as :

25 x 1=25

40 x 1= 40

25 x 2 = 50

40 x 2= 80

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Also 40 +25 = 65

40+2(25)= 90

2(40)+25= 105

2(40)+2(25)= 80+50=130

3(40)+25= 145

4(25)+40=140

Similarly we can get $150,$155,$160 also that tends to a general rule now that next amounts above 160 will be a multiplier of 5 as we have shown in last five steps here and this is where concept of induction starts implementing .

And general rule comprises here is n-25 where n is any multiplier of 5 above 160 that we get on adding one extra certificate offered by store.

So clearly it is example of a strong induction here.