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
find the numbers.
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.
Write a linear equation that models the packages offered by both companies.
If the average number of minutes used each month is 1,160, which company offers the better plan?
If the average number of minutes used each month is 420, which company offers the better plan?
How many minutes of talk-time would yield equal monthly statements from both companies?
The model for Company
A can be written as
This includes the variable cost of
plus the monthly service charge of $34. Company
B ’s package charges a higher monthly fee of $40, but a lower variable cost of
Company
B ’s model can be written as
If the average number of minutes used each month is 1,160, we have the following:
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.
If the average number of minutes used each month is 420, we have the following:
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.
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
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.
Check the
x- value in each equation.
Therefore, a monthly average of 600 talk-time minutes renders the plans equal. See
[link]
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?
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,
the
perimeter of a rectangle,
and the
volume of a rectangular solid,
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.
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
