[*]Professor Stashe awarded 500 certificates, for math and science. Girls won 2/3 of the math and 1/2 of the science certificates. If the number of girls who won for math was 50 more than 3/2 the number of girls who won for science, how many girls won for math?

i) Pick variables for each of the certificates; say, "m" for "math" and "s" for "science".

ii) What expression stands for the number of math certificates that the girls won?

iii) What expression stands for the number of science certificates that the girls won?

iv) What expression stands for "3/2 the number of girls who won for science"?

v) What expression stands for "50 more than" the previous amount?

vi) What equation stands for "the number of girls who won for math was" equal to the above amount?

vii) Given that there were 500 certificates in total, what expression stands for the number of science certificates,

*in terms of the certificates left after awarding the math certificates?*
viii) Substituting the expression from (vii) into the equation in (vi), what equation results?

ix) The equation in (viii) should be in terms only of the variable "m". Solve for the value of "m".

x) Back-solve for the number of girls who won math certificates.

If you get stuck, please reply showing your progress in following the above steps.