```Question 211233
midterm counts as 2/3 of the grade.
final counts as 1/3 of the grade.
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wendy scores only 48 on the midterm.
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her final score will be 2/3 * 48 + 1/3 * x
where x is her grade on the final.
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equation becomes:
y = 2/3 * 48 + 1/3 * x
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simplifying this equation, we get:
y = 32 + x/3
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multiply both sides of this equation by 3 to get:
3y = 96 + x
solve for x to get:
x = 3y - 96
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she needs to get a final grade that is between 70 and 79.
remember that x is what she needs to get on the final exam and y is what she needs to get as a final grade.
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let's find out what she needs for 70 first.
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let y = 70
equation of x = 3*y - 96 becomes:
x = 3 * 70 - 96
this becomes:
x = 210 - 96 = 114
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now let's find out what she needs for 79.
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let y = 79
equation of x = 3*y - 96 becomes:
x = 3 * 79 - 96
this becomes:
x = 237 - 96 = 141
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she would need 114 on the final exam to get a final score of 70.
she would need 141 on the final exam to get a final score of 79.
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let's plug these answers in the original formula to see if they make sense.
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she got 48 on the midterm.
she gets 114 on the final.
2/3 * 48 + 1/3 * 114 = 32 + 38 = 70 final grade
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she got 48 on the midterm.
she gets 141 on the final.
2/3 * 48 + 1/3 * 141 = 32 + 47 = 79 final grade
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