SOLUTION: It takes Akira 10 minutes to make a black and white drawing and 25 minutes for a color drawing. On Saturday he made a total of 9 drawings in 2 hours. Write and solve a system og eq

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Question 180281This question is from textbook Holt Algebra 1
: It takes Akira 10 minutes to make a black and white drawing and 25 minutes for a color drawing. On Saturday he made a total of 9 drawings in 2 hours. Write and solve a system og equations to determine how many drawings of each type akira made.
So do you need in the equation that it takes 2.5 times more to make a color drawing? What I don't get is how to make the variables. And to slove this equation do you solve it by using elmination or by substitution? This question is from textbook Holt Algebra 1

Answer by Mathtut(3670) (Show Source):
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It takes Akira 10 minutes to make a black and white drawing and 25 minutes for a color drawing. On Saturday he made a total of 9 drawings in 2 hours. Write and solve a system og equations to determine how many drawings of each type akira made.
So do you need in the equation that it takes 2.5 times more to make a color drawing? What I don't get is how to make the variables. And to slove this equation do you solve it by using elmination or by substitution?
:
First ask yourself what are they after. How MANY drawings of each type is made.That is your clue when it comes to varibles.
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so let b and c be the NUMBER of black-white and color paintings made respectively
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min. need to be converted to hours: so 10 min=1/6 hr and 25 min =5/12 hr
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b+c=9...........eq 1
1/6b+5/12c=2....eq 2
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rewrite eq 1 to b=9-c and plug that value into eq 2
:
(1/6)(9-c)+(5/12)c=2
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(9/6)-(1/6)c+(5/12)c=2
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18-2c+5c=24.........multiplied all terms by 12 to get rid of fractions
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3c=6
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number of colored paintings made
:
number of black-white paintings made