Question 130728This question is from textbook ALGEBRA FOR COLLEGE STUDENTS MARK DUGOPOLSKI
: Buying texts. melissa purchased an engllish text, a math text, and a chemistry text for a total of $276. the english text was $20 more than the math text and the chemistry text was twice the price of the math text. What is the price of each text?
This question is from textbook ALGEBRA FOR COLLEGE STUDENTS MARK DUGOPOLSKI
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let E represent the cost of the English text, M represent the cost of the Math text, and C
represent the cost of the Chemistry text.
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The problem tells you that the total cost for all three texts is $276. So if we add the three costs,
the total should be $276. We can write this in equation form as:
.
E + M + C = 276
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The problem then tells us that the English text cost $20 more than the Math text. So if we add
$20 to the cost of the Math text we know that the result is equal to the cost of the English
text. In equation form this is:
.
E = M + 20
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Therefore, in our equation for the total cost we can replace E with its equivalent value
of M + 20. This makes the cost equation become:
.
(M + 20) + M + C = 276
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Next we are told that the Chemistry text costs twice as much as the Math text. So if we double
the cost of the Math text, we have the price of the Chemistry text. In equation form this is:
.
C = 2*M
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So in our latest version of the equation for the total cost we can replace C with its
equivalent value of 2*M to get:
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(M + 20) + M + (2*M) = 276
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The three terms containing M are M, M, and 2M. Combine them to get 4M and the equation reduces to:
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4M + 20 = 276
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Get rid of the 20 on the left side by subtracting 20 from both sides to get:
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4M = 256
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Solve for M by dividing both sides of this equation by 4 and you have:
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M = 64
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So we know the Math text costs $64. The English text costs $20 more than that so it costs $84.
And the Chemistry text costs twice the Math text so it costs 2 times $64 or $128.
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Check: the costs of the three texts are English $84, Math $64, and Chemistry $128. Add them
and you get a total of $84 + $64 + $128 = $276. That checks. So our answer is correct.
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Hope this helps you to understand the problem and shows you a way that you can solve the
problem.
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