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Question 1137784: During a TV game show, picking a blue ball earn you 2 points and picking a red ball earn
5 points. The balls are to be picked blindly from a box and one contestant can pick
exactly 10 balls. A boy picked 10 balls and earned 35 points. How many red and blue
balls he picked?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
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 =  = 5.
Then from equation (1), y = 10 - 5 = 5.
ANSWER. 5 blue balls and 5 red balls.
CHECK. 5*2 + 5*5 = 35 balls. ! Correct !
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, read these two lessons
- Using systems of equations to solve problems on tickets
- Three methods for solving standard (typical) problems on tickets
in this site.
Although these lessons consider tickets, actually they are THE SAME problems as this one.
From these lessons, learn on how to solve such problems once and for all.
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 "Systems of two linear equations in two unknowns".
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