1. Michael and 6 friends went to the movies. There, they each bought movie tickets and a bag of popcorn to share among them all. Michael used the expression 7t + 4.50 to find the total cost. a) What is the variable and what does it represent in the expression? Explain.

The variable is t

t represent the cost of movie tickets

Step-by-step explanation:

Given:

Total cost = 7t + 4.50

The variable is t

Michael + 6 friends = 7 people

4.50 represent the cost of popcorn

t represent the cost of movie tickets

For instance,

If the cost of a movie tickets is $2

Then,

t = 2

Total cost = 7t + 4.50

= 7(2) + 4.50

= 14 + 4.50

= 18.50

Total cost = $18.50

step-by-step explanation:

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)