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?

Step-by-step explanation:

Given:

Equations

Girls who won certificates:

Multiply both sides by 12 to clear fractions

Substitute s

Girls who won math:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.