Word problem

Question

A custom bowling shirts company charges a design fee of $10 and sells each shirt for $25. The
total cost, C, can be represented by the function C(x) = 25x + 10, where x represents the number of
bowling shirts.

 

 

A-Without considering sales tax, if a bowling team paid $460, how many bowling shirts did they
buy? Solve your equation algebraically and answer in a complete sentence.

 

B-Find the equation of the line that passes through (0, -9) and has slope m = -8. Write your
equation in slope-intercept form.

 

C-Find the equation of the line that passes through the points (8, -2) and (5, 7). Write your
equation in point-slope form, slope-intercept form, and general form

 

Answer 1

A. Set the equation equal to 460 and solve for x.

 

25x + 10 = 460

25x = 450

x = 18

 

If a bowling team paid $460, then they ordered 18 shirts.

 

B. Use the point (y-intercept) and the slope to write the equation.

 

y = mx + b

y = -8x - 9

 

C. Find the slope between the two points.  Use one point to find the y-intercept.

 

m = (y₂ - y₁) / (x₂ - x₁) = (7 + 2) / (5 - 8) = 9 / -3 = -3

 

y = mx + b

7 = -3(5) + b

7 = -15 + b

22 = b

 

The equation in slope-intercept form is y = -3x + 22.

 

Use the slope-intercept form to rewrite in standard form:

 

y = -3x + 22

3x + y = 22

 

The equation in standard form is 3x + y = 22.

 

Use one point and the slope to write the equation in point-slope form:

 

(y - y₁) = m(x - x₁)

y - 7 = -3(x - 5)

 

The equation in point-slope form is y - 7 = -3(x - 5).