System of equations problem: from 1970-1990, the average annual per person consumption of whole milk in the us dropped from 103 to 43 quarts. the average annual consumption of low fat milk rose from 25 to 60 quarts. for which years did the consumption of lowfat milk exceed the consumption of whole milk?

From 1987 to 1990

Step-by-step explanation:

First we need to transform data into equations. Let's define x as years after 1970 (this means that x = 20 years represents 1990), y1 as average annual per person consumption of whole milk and y2 as the average annual consumption of low fat milk. Therefore, data can be expressed as

x     y1    y2

0    103  25

20  43   60

Regression of the data as equation of a line gives

b1 = 103 (y-intercept for whole milk case)

b2 = 25 (y-intercept for low fat milk case)

m1 = (43-103)/20 = -3 (slope for whole milk case)

m2 = (60-25)/20 = 1.75 (slope for whole milk case)

Then, y1 = -3*x+103 and y2 = 1.75*x + 25. These two equations intersect in one point from which low fat milk exceed the consumption of whole milk. In that point y1 = y2, so

-3*x+103 = 1.75*x + 25

103 - 25 = 1.75*x + 3*x

78 = 4.75*x

x = 78/4.75

x = 16.42

In years that is 1970 + 16.42 = 1986.42

answer: 1+1

step-by-step explanation: 1+1 is at least 2

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)