SOLUTION: If someone can help me understand on the steps of how to solve this word problem. Different weights. Professor Williamson counts his midterm as 2/3 of the grade and his final as

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Question 246153: If someone can help me understand on the steps of how to solve this word problem.
Different weights. Professor Williamson counts his midterm as 2/3 of the grade and his final as 1/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put Wendy’s range average between 70 and 79 inclusive? Compare to the previous exercise.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
2/3*48+1/3*x
2/3*48+1/3*x=70
32+x/3=70
subtract 32 from both sides
x/3=38
x=3*38=114
32+1/3*x=79
subtract 32
x/3=47
multiply by 3
x=3*47=141
between 114 and 141 inclusive
If it were 1/3 for the midterm and 2/3 for the final.
1/3*48+2/3*x=70
16+2/3x=70
2x/3=54
divide by 2
x/3=27
multiply by 3
x=3*27=81
1/3*48+2/3*x=79
16+2x/3=79
2x/3=63
multiply by 3
2x=189
divide by 2
x=94.5
between 81 and 94.5 inclusive