SOLUTION: "Solve each problem using a system of equations." a) How could you make 98¢ using exactly 30 nickels and pennies? b) Five pencils and four erasers cost 98¢. Two pencils and thr

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: "Solve each problem using a system of equations." a) How could you make 98¢ using exactly 30 nickels and pennies? b) Five pencils and four erasers cost 98¢. Two pencils and thr      Log On


   

Question 1155884: "Solve each problem using a system of equations."
a) How could you make 98¢ using exactly 30 nickels and pennies?
b) Five pencils and four erasers cost 98¢. Two pencils and three erasers cost 49¢. How much is a pencil?
Found 3 solutions by ikleyn, mananth, MathTherapy:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

To solve the problem, you write this system of 2 equations in 2 unknown


     N + P = 30     (1)     (counting coins)

    5N + P = 98     (2)     (counting money)


Next you subtract equation (1) from equation (2)

    4N = 98 - 30 = 68.


Finally, you divide both sides of the last equation by 4

     N           = 68/4 = 17.


ANSWER.  17 nickels and the rest (30-17) = 13 pennies.


CHECK.  17*5 + 13 = 85 + 13 = 98.   ! Correct !

Solved.

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For coin problems and their detailed solutions see the lessons in this site:
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
    - Three methods for solving standard (typical) coin word problems
    - More complicated coin problems
    - Solving coin problems mentally by grouping without using equations
    - Non-typical coin problems
    - Santa Claus helps solving coin problem
    - OVERVIEW of lessons on coin word problems

You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.

A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

Read them attentively and become an expert in this field.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Coin problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!

n+p=30 (coins)--------------1
5n+p=98 (value)1 ----------2
Subtract 1 from 2
we get 4p = 68
p= 17
if p=17 n=3
Nickels -17
Pennies 3
CHECK
17*5 + =98

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

"Solve each problem using a system of equations."
a) How could you make 98¢ using exactly 30 nickels and pennies?
b) Five pencils and four erasers cost 98¢. Two pencils and three erasers cost 49¢. How much is a pencil?
What the other person told you is WRONG!! 17 pennies & 3 nickels do not make $0.98, and neither does 17 nickels and 3 pennies.

I don't know why these people keep misleading others by almost always giving WRONG answers!