Explanation:
a)
100% = 16.25
1% = 100%/100 = 16.25/100 = 0.1625
the discount was $16.25 - $13.00 = $3.25.
how many % is that ?
well, it is a many % as how many times 1% (0.1625) fits into 3.25.
so,
3.25 / 0.1625 = 20
therefore, the coupon was for 20% off.
b)
30% off means he paid 70% of the normal price.
70% = 10.31
1% = 70%/70 = 10.31/70 = 0.147285714...
100% = 1%×100 = 0.147285714... × 100 = 14.72857143...
so, rounded to the nearest cent the normal price for a medium pizza is $14.73
FYI - the direct method would be to divide the discounted price by the %, so, 10.31 / 0.7 ≈ 14.73
but the reason for this shortcut is in the detailed steps explained above.
c)
as we have seen in a) and b), a large pizza after 20% discount is $13, and a medium pizza after 30% discount is $10.31. both is too much for the available $10 (and even less discount).
so, the only chance is a small pizza.
15% discount means to pay 85%.
100% = 11.6
1% = 0.116
85% = 1%×85 = 9.86
he can afford max. a small pizza after 15% discount for $9.86 with his $10.
to calculate in the other direction : with a 15% coupon it means
85% = 10
1% = 10/85 = 0.117647059...
100% = 1%×100 = 11.76470588... ≈ 11.76
with a 15% coupon and $10 he can afford to buy something with a normal prize of max. $11.76