Question 1171212
.
Jesse and Adam are both selling items to raise money for Baseball uniforms. They are each selling
two items: chocolate bars and candles. Jesse sells 12 chocolate bars and 7 candles and makes a
total of $94. Adam sells 24 chocolate bars and 5 candles and makes a total of $98. How much does
one chocolate bar and one candle cost?
~~~~~~~~~~~~~~



<pre>
    12H + 7C = 94       (1)   (H stands for chocolate bars;  C stands for candles)

    24H + 5C = 98       (2)


Multiply equation (1) by 2 (both sides).  Keep equation (2) as is.  You will get


    24H + 14C = 188     (1') 

    24H +  5C =  98     (2')


Now subtract equation (2') from equation (1').  

The terms "24H" will cancel each other, and you will get a single equation in one unknown C

          14C - 5C = 188 - 98

             9C    =  90

              C    =  90/9 = 10.


Thus the cost of each candle is $10.


To find another unknown, H, substitute the found valu C into equation (1).  You will get

    12*H + 7*10 = 94

    12H         = 94 - 70 = 24

      H                   = 24/12 = 2.


<U>ANSWER</U>.  $2 per chocolate bar and $10 for each candle.
</pre>

Solved.


From my solution, learn on how the ELIMINATION method works.


............


I remember that in my previous post I showed you, how to solve this problem MENTALLY.


So, now you know TWO methods, which is good (!)


------------


On solving systems of linear equations in two unknowns see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF = http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-system-of-two-eqns-by-the-Subst-method.lesson>Solution of a linear system of two equations in two unknowns by the Substitution method</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF = http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-Elimination-method.lesson>Solution of a linear system of two equations in two unknowns by the Elimination method</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-using-det.lesson>Solution of a linear system of two equations in two unknowns using determinant</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of a linear system of two equations in two unknowns</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Useful-tricks-when-solving-systems-of-2-eqns-in-2-unknowns-by-the-Subst-method.lesson>Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solving-word-probs-using-linear-systems-of-two-eqns-with-two-unknowns.lesson>Solving word problems using linear systems of two equations in two unknowns</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Word-problems-that-lead-to-a-simple-system-of-two-equations-in--wo-unknowns.lesson>Word problems that lead to a simple system of two equations in two unknowns</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/Oranges-and-Grapefruits.lesson >Oranges and grapefruits</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-Tickets.lesson>Using systems of equations to solve problems on tickets</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Three-methods-for-solving-standard-typical-problem-on-tickets.lesson>Three methods for solving standard (typical) problems on tickets</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-SHARES.lesson>Using systems of equations to solve problems on shares</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-investment.lesson>Using systems of equations to solve problems on investment</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Two-mechanics-work-on-a-car.lesson>Two mechanics work on a car</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/The-Robinson-family-and-the-Sanders-family-each-used-their-sprinklers-last-summer.lesson>The Robinson family and the Sanders family each used their sprinklers last summer</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Roses-and-violets.lesson>Roses and vilolets</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/Counting-calories-and-grams-of-fat-in-combined-food.lesson>Counting calories and grams of fat in combined food</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/A-theater-group-made-appearances-in-two-cities.lesson>A theater group made appearances in two cities</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/How-to-algebreze-and-to-solve-this-problem-on-2-eqns-in-2-unknwns.lesson>HOW TO algebreze and solve this problem on 2 equations in 2 unknowns</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/One-unusual-problem-to-solve-using-system-of-two-equations.lesson>One unusual problem to solve using system of two equations</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Solving-mentally-word-problems-on-two-equations-in-two-unknowns-NEW.lesson>Solving mentally word problems on two equations in two unknowns</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Systems of two linear equations in two unknowns</U>".



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.