Question

Professor Stache awarded 500 certificates, some for math, and some for science. Girls won 2/3 of the math certificates 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?

Answer 1

• 200

Explanation:

Given:

• Total certificates = 500
• Math = m
• Science = s

Equations

• m+s = 500 ⇒ s = 500 - m

Girls who won certificates:

• 2/3m = 50 + 3/2*1/2s
• 2/3m = 50 + 3/4s

Multiply both sides by 12 to clear fractions

• 8m = 600 + 9s

Substitute s

• 8m = 600 + 9(500 - m)
• 8m = 600 + 4500 - 9m
• 17m = 5100
• m = 5100/17
• m =300

Girls who won math:

• 2/3*300 = 200