2.4 mil libs price sold 5.50 per lb amd 4.8 mil libs 4.50 ld. what linear function 1(p) expresses the amount

Question

of almonds sold as a function of the price per pound

Answer 1

Let me restate this cryptic question.

2.4 million lb (pounds) of almonds are sold when the selling price is $5.50 per lb.

4.8 million lb (pounds) of almonds are sold when the selling price is $4.50 per lb.

What linear function expresses the amount of almonds sold as a function of the price per pound?

Answer:

Here selling price is the independent variable (x-axis) and almond sales in pound is a function of price (y-axis).

We can see that as price of almonds goes up, its sales decrease. So we expect a negative slope for this linear equation line.

Here we need to find the equation of line that passes through two points (x1, y1)=(5.5, 2.4) and (x2, y2)=(4.5, 4.8).

Solution using equation of line in 2 points form

(y-y1)/(y1-y2) = (x-x1)/(x1-x2) substitute co-ordinates of above two points in this equation

(y - 2.4)/(2.4 - 4.8) = (x - 5.5)/(5.5 - 4.5)

(y-2.4)/(-2.4) = (x - 5.5)/1

(y-2.4)/(-2.4) * -2.4 = (x - 5.5)/1 * -2.4 multiply both sides by -2.4

y - 2.4 = -2.4 (x - 5.5)

y - 2.4 = -2.4x + 13.2 ...remember when you multiply 2 negative numbers, you get a positive number

add 2.4 to both sides

y - 2.4 + 2.4 = -2.4x + 13.2 + 2.4

y = -2.4x + 15.6 (where x is price per pound of almonds and y is almonds sold in million pounds)

Alternative method by using slope-intercept form

Equation of line is given by

y = mx + c where m is the slope and c is the y-intercept

Slope of line passing through two points (x1, y1) and (x2, y2) is m = (y1-y2)/(x1-x2)

y = mx + c ....substitute above value of slope m.

y = (y1-y2)/(x1-x2)*x + c where c is the constant y-intercept

Substitute values of (x1, y1) and (x2, y2) in this equation

y= (2.4 - 4.8)/(5.5 - 4.5) *x +c

y=-2.4/1 *x +c y=-2.4x+c...................(1)

substitute (x1, y1) = (5.5, 2.4) in above equation to solve for c

2.4 = -2.4*5.5 +c

2.4 = -13.2 +c ....add 13.2 on both sides to get value of c

2.4 + 13.2 = -13.2 +c + 13.2

15.6 = c Substitute this value in equation (1) above to get

y = -2.4x + 15.6

Check:

We see that slope of the linear equation is negative. This is as expected.

substitute x = 5.5 in above equation and see if you get y = 2.4

substitute x = 4.5 in above equation and see if you get y = 4.8

Answer 2

The total value of the almonds sold should be:

(2.4 mil)(5.50 ea) + (4.8 mil)(4.50 ea) = 34.8 million dollars.

If we want a function of lbs of almonds sold as a function of price, we want the ratio (lbs sold)/(total price), so we want

(2.4 + 4.8 mil)/[(2.4 mil)(5.50 ea) + (4.8 mil)(4.50 ea)] = 0.2183908 lbs/$.