Question 1137784
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<pre>
Let x = # of blue balls, y = # of red balls.


From the condition, you have these 2 equations


     x +  y = 10        (1)    (counting balls)

    2x + 5y = 35       (2)     (counting points)


From equation (1), express  y = 10 - x  and substitute it into equation (2), You will get


    2x + 5*(10-x) = 35.


Express x and calculate answer


    x = {{{(35 - 5*10)/(2 - 5)}}} = 5.


Then from equation (1),  y = 10 - 5 = 5.


<U>ANSWER</U>.  5 blue balls and 5 red balls.


<U>CHECK</U>.   5*2 + 5*5 = 35 balls.   ! Correct !
</pre>

The problem solved using 2-equation setup and the Substitution method.


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There are many other ways to solve this problem.


If you want to learn this subject, &nbsp;read these two lessons

&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>

in this site.


Although these lessons consider tickets, &nbsp;actually they are THE SAME problems as this one.

From these lessons, &nbsp;learn on how to solve such problems once and for all.


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>".