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| − | ==Problem 12==
| + | #REDIRECT [[2007 AMC 10B Problems/Problem 16]] |
| − | A teacher gave a test to a class in which <math>10%</math> of the students are juniors and <math>90%</math> are seniors. The average score on the test was <math>84</math>. The juniors all received the same score, and the average score of the seniors was <math>83</math>. What score did each of the juniors receive on the test?
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| − | <math>\mathrm {(A)} 85</math> <math>\mathrm {(B)} 88</math> <math>\mathrm {(C)} 93</math> <math>\mathrm {(D)} 94</math> <math>\mathrm {(E)} 98</math>
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| − | ==Solution==
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| − | Taking a weighted average
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| − | <math>(90\%)(83) + (10\%)(x) = 84</math> where x is the Juniors' score
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| − | <math>\begin{align*}x & = 10(84 - .9(83) \\
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| − | & = 840 - 9(83) \\
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| − | & = 93 \Rightarrow \mathrm {(C)}</math>
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