Question 928206: A jar containing only nickels and dimes contains a total of 14 coins. the value of all the coins in the jar is $1.10. write and graph a system of equations to find the amount of nickels and dimes that are in the jar. Identify the variables, write the equations, and solve the system using graphing, elimination, and substitution methods. Write complete answers. Show all your work step by step. Write a short explanation about which will be the best method to solve the problem.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = number of nickels
y = number of dimes
---
x + y = 14
5x + 10y = 110
---
put the system of linear equations into standard form
---
x + y = 14
5x + 10y = 110
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = number of nickels = 6
y = number of dimes = 8
---
by elimination:
---
-10(x + y = 14)
5x + 10y = 110
---
-10x - 10y = -140
5x + 10y = 110
---
add the two equations:
---
-5x = -30
x = 6
x + y = 14
y = 14 - x
y = 14 - 6
y = 8
---
solution by elimination:
x = number of nickels = 6
y = number of dimes = 8
---
by substitution:
---
x + y = 14
y = 14 - x
---
5x + 10y = 110
5x + 10(14 - x) = 110
5x + 140 - 10x = 110
-5x = -30
x = 6
y = 14 - x
y = 14 - 6
y = 8
---
solution by substitution:
x = number of nickels = 6
y = number of dimes = 8
---
by graphing:
---
line A:
x + y = 14
y = -x + 14
slope = -1
y-intercept = (0,14)
graph it ...
---
line B:
5x + 10y = 110
10y = -5x + 110
y = (-5x + 110)/10
y = (-5/10)x + (110/10)
y = (-1/2)x + 11
slope = -1/2
y-intercept = (0,11)
graph it ...
---
the graphs of the lines intercept at the point (6,8)
---
solution by graphing:
x = number of nickels = 6
y = number of dimes = 8
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
|
|
|
