Nine more shows.

Complete Solution:

You can consider this problem in terms of minutes or in units of half-hour shows. Using only the SP setting, the tape can record 120 minutes of shows. If one 30 minute show has already been recorded, 1/4 of the tape has been used.

 Type of Setting Minutes Used Total Minutes on Tape Portion of Tape Used SP 30 120 30/120 or 1/4 EP (1/4) × 360, or 90 360 90/360 or 1/4

With 1/4 of the tape filled, 90 minutes of EP has been used, so that there are 360-90 or 270 minutes left. At 30 minutes per show, nine additional shows can be taped.

If you are using half-hour units, there are four half-hour shows on SP in two hours. One half-hour show used 1/4 of the tape. Three-fourths of the tape is left. With EP, you can do 12 half-hour shows, and then you have enough tape for 3/4 × 12, or 9 shows remaining.

Yet another way to consider this problem is to use proportions as follows:

Because 3 × 120 = 360 and 3 × 30 = 90, there are 90 minutes used on the EP setting, so that there are 360 - 90, or 270 minutes available which allows for 9 thirty-minute shows on EP.

Similarly 30 × 360 = 120 × (x number of minutes), so the number of minutes is 90.

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