# Solving Applied Problems: Two Equations?

problem 1

Rudy must play 12 commercials during his 1-hour show. Each commercial is either 30 seconds or 60 seconds long. If the total commercial time during that hour is 10 minutes, how many commercials of each type does rudy play?

Relevance

There are a 30s commercials and b 60s commercials

a+b = 12

30a+60b=10*6

30a + 60b = 600

multiply the first equation by 30

30a+30b=360

subtract this from the second equation

30b=240

b = 8

substitute this back into the 1st equation

a+8=12

a=4

• You have two equations here. If x is the number of 30 second commercials and y the number of 60 second commercials, x + y is 12 and 30*x + 60*y = 10*60, or 600. So I'd recommend substitution. Y = 12 - x. 30 * x + 720 - 60*x = 600. 30 * x = 120. X = 4, and therefore y = 8. You can check this: 4 * 30 + 8 * 60 = 600 seconds, or 10 minutes.

• Anonymous

Let x= the number of 30 second commercials

Let y= the number of 60 second commercials

x+y = 12

.5x+y = 10 (i used .5 and 1 to keep everything in minutes)

x=4, y=8

4 30-second commercials, 8 minute commercials

• If we let x be the number of 30 second commercials, then 12-x will be the number of 60 second commercials (if he plays x 30 second ones and needs to play 12 total, then 12-x will be the number of 60 second ones).

10 minutes of commercials total is 600 seconds of commercials. (10min x 60s/min).

30x = the amount of time used by 30 second commercials

60(12-x) = the amount of time used by 60 second commercials.

So,

30x + 60(12-x) = 600

First, to make smaller numbers factor out 30:

30[ x + 2*(12-x) ] = 600

x + 2(12-x) = 20

x + 24 - 2x = 20

24 - x = 20

x = 24-20 =4

So, 4 30 second commercials and 12-4= 8 60 second commercials.

• .5x+12-x=10 .5 is 30 seconds

combine like terms

-.5x+12=10

subtract 12 from both sides

-.5x=-2

divide both sides by -.5

x=4 4 30-second commercials which leaves 8 60-second ones which adds up to 10 minutes.

Source(s): math teacher