SOLUTION: 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 ni
Algebra.Com
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
RELATED QUESTIONS
a jar containing only nickels and dimes contains a total of 50 coins. the value of all... (answered by jim_thompson5910)
A jar containing only nickels and dimes contains a total of 51 coins. The value of all... (answered by JulietG)
a jar containing only nickels and dimes contains 60 coins. The value of all the coins in... (answered by checkley77)
A jar containing only nickels and dimes contains a total of 749 coins. The value of the... (answered by TimothyLamb)
a jar of coins contains only nickels and dimes. There are 500 coins in the jar and the... (answered by JulietG)
A jar containing only quarters and dimes. Contains a total of 65 coins. The value of all... (answered by jorel1380)
A jar contains 70 coins, all of which are nickels and
dimes. The total value of the... (answered by ikleyn)
A jar contains 70 coins, all of which are nickels and
dimes. The total value of the... (answered by Boreal)
A jar filled with only dimes and quarters contains a total of 58 coins. The value of all... (answered by CubeyThePenguin)
sandy has a total of 35 coins in her money jar. If Sandy's jar contains only nickels and... (answered by Edwin McCravy)