30 girls and boys have planned for a picnic. There is a ratio of 3 girls to 7 boys. How many boys are there?
2 answers:
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Answer:
$4
Step-by-step explanation:
The two purchases can be written in terms of the cost of an adult ticket (a) and the cost of a student ticket (s):
7a +16s = 120 . . . . . . . . price for the first purchase
13a +9s = 140 . . . . . . . . price for the second purchase
Using Cramer's rule, the value of s can be found as ...
s = (120·13 -140·7)/(16·13 -9·7) = 580/145 = 4
The cost of a student ticket is $4.
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<em>Comment on Cramer's Rule</em>
Cramer's rule is particularly useful for systems that don't have "nice" numbers that would make substitution or elimination easy methods to use. If you locate the numbers in the equation, you can see the X-patterns that are used to compute the numerator and denominator differences.
The value of a is (16·140 -9·120)/(same denominator) = 1160/145 = 8. I wanted to show you these numbers so you could see the numerator X-pattern for the first variable.
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Of course, graphical methods can be quick and easy, too.
