Generalize the average test grade. Suppose Jane has an average of G after n tests. What average score does she need on the next m tests to average H for all m + n tests?

t1 = test #1, t2 = test #2, ...

(t1 + t2 + ... + tn)/n = G

(t1 + t2 + ... + tn) = n*G

((t1 + t2 + ... + tn) + (tn+1 + tn+2 + ... + tm))/(m+n) = H

(n*G + (tn+1 + tn+2 + ... + tm))/(m+n) = H

n*G + (tn+1 + tn+2 + ... + tm) = (m+n)*H

(tn+1 + tn+2 + ... + tm) = (m+n)*H - n*G

(tn+1 + tn+2 + ... + tm)/m = ((m+n)*H - n*G)/m

((m+n)*H - n*G)/m is my answer but I'm a little unsure of this. Any help would be greatly appreciated!!!