<< 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

it is the relatively stable flow of income
Chidubem Reply
what is circular flow of income
Divine Reply
branches of macroeconomics
SHEDRACK Reply
what is Flexible exchang rate?
poudel Reply
is gdp a reliable measurement of wealth
Atega Reply
introduction to econometrics
Husseini Reply
Hi
mostafa
hi
LEMLEM
hello
Sammol
hi
Mahesh
bi
Ruqayat
hi
Ruqayat
Hi fellas
Nyawa
hey
Sammol
hi
God
hello
Jahara
Good morning
Jorge
hi
abubakar
hi
Nmesoma
hi
Mahesh
Hi
Tom
Why is unemployment rate never zero at full employment?
Priyanka Reply
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
Rushawn Reply
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost 6% more than previous year? Provide with reasoning.
Geetha Reply
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
Alii Reply
what is the problem of macroeconomics
Yoal
Economic growth Stable prices and low unemployment
Ephraim
explain inflationcause and itis degre
Miresa Reply
what is inflation
Getu
increase in general price levels
WEETO
Good day How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200. Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
Chisomo Reply
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
Thapase Reply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
Mercy Reply
Hi
Isiaka
Hi
Geli
hy
Man
👋
Bahunda
hy how are you?
Man
ys
Amisha
how are you guys
Sekou
f9 guys
Amisha
how are you guys
Sekou
ys am also fine
Amisha
fine and you guys
Geli
from Nepal
Amisha
nawalparasi district from belatari
Amisha
nd u
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ma management ho
Amisha
ahile becheclor ho
Amisha
hjr ktm bta ho ani k kaam grnu hunxa tw
Amisha
belatari
Amisha
1st year ho
Amisha
nd u
Amisha
ahh
Amisha
kaha biratnagar
Amisha
ys
Amisha
kina k vo
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9 no Mpc is greater than 1 Y=100+.9Y+50 Y-.9Y=150 0.1Y/0.1=150/0.1 Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output? discuss your answer using appropriate graph.
Galge Reply
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 3

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




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