<< Chapter < Page Chapter >> Page >

Find a linear equation to solve for the following unknown quantities: One number is three more than twice another number. If the sum of the two numbers is 36 , find the numbers.

11 and 25

Got questions? Get instant answers now!

Setting up a linear equation to solve a real-world application

There are two cell phone companies that offer different packages. Company A charges a monthly service fee of $34 plus $.05/min talk-time. Company B charges a monthly service fee of $40 plus $.04/min talk-time.

  1. Write a linear equation that models the packages offered by both companies.
  2. If the average number of minutes used each month is 1,160, which company offers the better plan?
  3. If the average number of minutes used each month is 420, which company offers the better plan?
  4. How many minutes of talk-time would yield equal monthly statements from both companies?
  1. The model for Company A can be written as A = 0.05 x + 34. This includes the variable cost of 0.05 x plus the monthly service charge of $34. Company B ’s package charges a higher monthly fee of $40, but a lower variable cost of 0.04 x . Company B ’s model can be written as B = 0.04 x + $ 40.
  2. If the average number of minutes used each month is 1,160, we have the following:

    Company  A = 0.05 ( 1.160 ) + 34 = 58 + 34 = 92 Company  B = 0.04 ( 1 , 1600 ) + 40 = 46.4 + 40 = 86.4

    So, Company B offers the lower monthly cost of $86.40 as compared with the $92 monthly cost offered by Company A when the average number of minutes used each month is 1,160.

  3. If the average number of minutes used each month is 420, we have the following:

    Company  A = 0.05 ( 420 ) + 34 = 21 + 34 = 55 Company  B = 0.04 ( 420 ) + 40 = 16.8 + 40 = 56.8

    If the average number of minutes used each month is 420, then Company A offers a lower monthly cost of $55 compared to Company B ’s monthly cost of $56.80.

  4. To answer the question of how many talk-time minutes would yield the same bill from both companies, we should think about the problem in terms of ( x , y ) coordinates: At what point are both the x- value and the y- value equal? We can find this point by setting the equations equal to each other and solving for x.

    0.05 x + 34 = 0.04 x + 40 0.01 x = 6 x = 600

    Check the x- value in each equation.

    0.05 ( 600 ) + 34 = 64 0.04 ( 600 ) + 40 = 64

    Therefore, a monthly average of 600 talk-time minutes renders the plans equal. See [link]

Coordinate plane with the x-axis ranging from 0 to 1200 in intervals of 100 and the y-axis ranging from 0 to 90 in intervals of 10.  The functions A = 0.05x + 34 and B = 0.04x + 40 are graphed on the same plot
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find a linear equation to model this real-world application: It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The company has monthly operating expenses of $350 for utilities and $3,300 for salaries. What are the company’s monthly expenses?

C = 2.5 x + 3 , 650

Got questions? Get instant answers now!

Using a formula to solve a real-world application

Many applications are solved using known formulas. The problem is stated, a formula is identified, the known quantities are substituted into the formula, the equation is solved for the unknown, and the problem’s question is answered. Typically, these problems involve two equations representing two trips, two investments, two areas, and so on. Examples of formulas include the area    of a rectangular region, A = L W ; the perimeter    of a rectangle, P = 2 L + 2 W ; and the volume    of a rectangular solid, V = L W H . When there are two unknowns, we find a way to write one in terms of the other because we can solve for only one variable at a time.

Questions & Answers

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
Naveen
what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
Vinay Reply
10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
Payal Reply
prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
Tejas Reply
why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
Ayushi Reply
Please you teach
Dua
Yes
ahmed
Thank you
Dua
give me treganamentry question
Anshuman Reply
Solve 2cos x + 3sin x = 0.5
shobana Reply
Practice Key Terms 3

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask