Question

Homewood Middle School has 1200 students, and 730 of these students attend a summer picnic. If two-thirds of the girls in the school and one-half of the boys in the school attend the picnic, how many girls attend the picnic?

Answer 1

520

Explanation:

i also got the problem and got it wrong - i found the answer is 520

Answer 2

520 girls attended the picnic

Explanation:

Hello

step 1

Let

Homewood middle school total students=1200

A=unknown=total of girls

(2/3)A=total girls attended the picnic

B=unknown= total of boys

(1/2)B=total boys attended the picnic

step2

replace

`A+B=1200\ equation (1) \\(2A)/(3)+(B)/(2)=730\ equation(2)\\`

Step 3

find A and B

from equation (1)

`A=1200-B\ equation\ (3)\\\\`

from equation (2)

`(2A)/(3)+(B)/(2)=730\\(2A)/(3)=730-(B)/(2)\\A=(730-(B)/(2))*(3)/(2) \\1200-B=1095-(3B)/(4)\\A=A\\-B+(3B)/(4)=1095-1200\\-(B)/(4)=-105\\ B=420\\\\hence\\\\A=1200-B\\A=1200-420\\A=780`

total girls attended the picnic=(2/3)A=(2/3)780=520

520 girls attended the picnic