In a talent show of singing and comedy acts, singing acts are 4.5 minutes long and comedy acts are 3.5 minutes long. The show has 14 total acts and lasts 59 minutes. How many singing acts and comedy acts are there?

Step-by-step explanation:

Let the number of singing act be x

Let the number of comedy act be y

If the total act is 14, then;

x+y = 14 1

If singing acts are 4.5 minutes long and comedy acts are 3.5 minutes long and the acts lasts 59 minutes, then:

4.5x + 3.5y = 59 2

Solve both equation simultaneously for x and y

x+y = 14

45x+35y = 590

x+y = 14 *9

9x+7y = 118 1

9x+9y = 126

9x+7y = 118

Subtract both equations

9y-7y = 126-118

2y = 8

y = 8/2

y = 4

Substitute y = 4 into equation 1;

From 1: x+y = 14

x+4 = 14

x = 14-4

x =10

Hence there are 10 singing acts and 4 comedy acts in the show

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

7

step-by-step explanation: