My kid answered this question by guessing and checking. The teacher took points off for not using a formula. My kid insisted I solve the problem using a formula. I took a stab at it


>Let the number of shirts sold be n. Note that:

>n = 16q + r

>where q and r are the quotient and remainder respectively of dividing n by 16. Both q and r are positive integers and 0<=r<=15.

>Now our total money earned is

>364 = 4n + 20q

>Elimination q with the substitution q = (n-r)/16 and some simplification we have

>1456 = 21n - 5r

>which is a linear Diophantine equation with solution

>n = 5m + 1, r = 21m - 287 for some integer m.

>Since 0 <= r <= 15 we must have m = 14.

>Hence n = 5*14 + 1 = 71.

My kid said he didn't know wtf I did at all. He was confused about everything I did. The kid doesn't seem to understand division. The whole quotient remainder thing seemed to throw him off and he didn't know what GCD was. He also said I didn't use a formula and kept asking what the formula for guess and check was. In the end I just had him write out his guess and check calculations out. Is my kid retarded or is the school failing him? Or am I retarded and there is a "formula" for this problem?