![greyxxamber](/avatars/42100.jpg)
greyxxamber
01.12.2020 •
Mathematics
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $3000. What was the rate charged per hour by each mechanic if the sum of the two rates was $175 per hour?
Solved
Show answers
More tips
- H Health and Medicine How to perform artificial respiration?...
- H Health and Medicine 10 Tips for Avoiding Vitamin Deficiency...
- F Food and Cooking How to Properly Cook Buckwheat?...
- F Food and Cooking How Many Grams Are In a Tablespoon?...
- L Leisure and Entertainment Carving: History and Techniques for Creating Vegetable and Fruit Decorations...
- P Photography and Videography How to Choose the Perfect Photo Paper for Your Images?...
- H Health and Medicine What vaccines do children need?...
- H Health and Medicine Reasons for the Appearance of Warts: Everything You Need to Know...
- A Art and Culture How to Learn Screaming: Step-by-Step Guide for Beginners...
- H Health and Medicine Contraceptive Pills After 35: The Importance Of Choosing The Right Medication...
Answers on questions: Mathematics
- M Mathematics G(x) = 4x + 5 h(x)=-3x-3 Find (g•h) (x)...
- M Mathematics Which is the graph of the equation below? y=3/4x-2...
- M Mathematics Set up a proportion and solve the following! Two out of five students in the ninth grade have braces. If there are 325 students in the ninth grade, how many have braces?...
- M Mathematics Solve (10b+7b^2-6b^3)-(12b^2-3b^3)...
- M Mathematics H everyoneejhfgwds,ncxzmjke,sdfzxckjh,nm...
- M Mathematics IF U ANSWER THIS RIDDLE UR AWESOME ill give thanks, thanks to account, brainlest, and 5 star rating...
- M Mathematics This table shows a linear relationship. x 6 12 18 24 30 y 252 504 756 1008 1260 Based on the information in this table, which equation can be used to model the relationship...
- M Mathematics A car travels 350 miles in 5 hours at a constant rate. At this rate, how far will the car travel in 8 hours?...
- M Mathematics A brainliest will be rewarded to the best answer! Which expression has a value of 11? A. 13 - 5 - 3 B. 1 + (8 x 2) C. 5 + 2 x (4 - 1) D. 15 - 1 + (6 ÷ 2)...
- M Mathematics 1. Which equation is true for all pairs of values in the table? * 1 point X -1 1 2 3 у O 4 6 8 O y = 2x - 2 O y = 2x + 2 O y = 4x O y = x + 3...
Ответ:
the rate charged per hour by the first mechanic is 75 $/hr and the rate charged per hour by the second mechanic is 100 $/hr.
Step-by-step explanation:
A system of equations is a set of two or more equations in various unknowns in which you want to find a common solution.
So, first of all it is convenient to define the system variables:
x= the rate charged per hour by the first mechanicy= the rate charged per hour by the second mechanicIf the sum of the two rates were $ 175 per hour, then the mathematical expression that represents this situation is: x + y= 175
You know that the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Then the amount of money won by the first and second mechanic respectively is expressed by 20*x and 15*y. Together they charged a total of $3000, then 20*x + 15*y=3000
So, the system of equations to solve is:
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
There are several methods for solving a system of equations. One of them is the substitution method, which consists of solving or isolating one of the unknowns (for example, x) and substituting its expression in the other equation. In this way, you obtain an equation of the first degree with the other unknown. Once solved, you must calculate the value of x by substituting the already known value of y.
In this case, you isolate the variable x from the first expression:
x= 175 - y
Replacing this expression in the second equation:
20*(175 - y)+15*y=3000
and solving you get:
20*175 -20*y +15*y=3000
3500 -20*y +15*y=3000
3500 -5*y=3000
-5*y=3000 -3500
-5*y= -500
y= (-500)÷(-5)
y= 100
So:
x=175 -y
x=175 -100
x=75
Then the rate charged per hour by the first mechanic is 75 $/hr and the rate charged per hour by the second mechanic is 100 $/hr.
Ответ:
The rate charged by the first mechanic is $75/h and by the second is $100/h.
Step-by-step explanation:
We have that the two mechanics charged a total of $3000:
The sum of the rate of the two mechanics was $175 per hour:
The rate of the first (A) and second (B) mechanic is:
By entering equation (3) and (4) into (2):
Now, by entering equation (1) into (5) we have:
Now, for the first mechanic we have:
Finally, from equation (3) and (4) we can find the rate charged per hour by each mechanic:
Therefore, the rate charged by the first mechanic is $75/h and by the second is $100/h.
I hope it helps you!
Ответ:
6.28 centimeters
Step-by-step explanation:
r = 1/2d = 1/2 × 4 = 2 centimeters