Question

Zöe schedules advertising for a radio station. She must fill 12 minutes each hour with 30 second ads and 60 second ads. Zöe sold twice as many 60 second ads as she did 30 second ads. She defines x as the number of 30 second ads and y as the number of 60 second ads that she sold. Zöe writes the system    and . Which statement identifies Zöe’s error and the correction that is needed?  Zöe used seconds to measure time for each ad, but she used minutes for the total. She should have used . Zöe set up an equation that would translate to “twice the number of 30 second ads = the number of 60 second ads.”  She should have used . Zöe compared the number of 30 second ads to the number of 60 second ads without  including the total number of ads. She should have used . Zöe did not include the whole hour in the total time. She should have used .

Answer 1

I cannot see Zoe's work to explain the error, but the correct method of solving is listed:

x is the number of 30-second ads
y is the number of 60-second ads

x+y=12(60)=720 would be the first equation; this is because while the ads together make 12 minutes, the ad times are in seconds.  This means we must multiply 12 by 60.

y=2x is the second equation

Our system is then
x+y=720
y=2x

We will use substitution to solve this.  Plug 2x in place of y in the first equation:
x+2x = 720

Combine like terms:
3x = 720

Divide both sides by 3:
3x/3 = 720/3
x = 240

Substitute this value in for x in the second equation:
y=2(240)
y=480