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# Tom took five math tests and got an integer score on each of them. He never scored higher than 90, and his lowest score was the fourth test.

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Tom took five math tests and got an integer score on each of them. He never scored higher than 90, and his lowest score was the fourth test. If his average score, rounded to the nearest integer, was 82, what is the lowest possible score he could have gotten on the fourth test?

Guest Jun 28, 2015

#5
+94105
+8

Easier way:

90*4=360

81.5*5=407.5

lowest possible for test 4 = 407.5-360=47.5

But lowest possible integer result is 48

Melody  Jul 1, 2015
#1
+423
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For the lowest possible on a single test to still result in an average value that is particularly high, then we give the other tests the highest possible value and see what we can get:

89 is the highest possible value, thus:

82 = (4*89 + fourth test) / 5

82 = (356 + fourth test) / 5

410 = 356 + fourth test

fourth test = 410 - 356

fourth test = 54

Sir-Emo-Chappington  Jun 28, 2015
#2
+92674
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Notice that he never scored higher than 90 on any test.......but......he could have scored 90 on four of them....so....we might have something like this......

[90 + 90 + 90 + x + 90] / 5   = 82     multiply both sides by 5  and simplify the left side

360 + x  =  410     subtract 360 from both sides

x = 50      and this would be his lowest score

CPhill  Jun 28, 2015
#3
+94105
+8

Tom took five math tests and got an integer score on each of them. He never scored higher than 90, and his lowest score was the fourth test. If his average score, rounded to the nearest integer, was 82, what is the lowest possible score he could have gotten on the fourth test?

The average could have been between 81.5 and 82.5

Say he scored 90 on all the other tests that is a total of 360 for the four other tests

so

$$\\81.5\le \frac{360+fourth}{5}<82.5\\\\ 407.5\le 360+fourth<412.5\\\\ 47.5\le fourth<52.5\\\\ But all the scores were integers so\\\\ the lowest possible score for the fourth test was  48$$

Melody  Jul 1, 2015
#4
+94105
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Any more reduction - any takers ?      LOL

Melody  Jul 1, 2015
#5
+94105
+8

Easier way:

90*4=360

81.5*5=407.5

lowest possible for test 4 = 407.5-360=47.5

But lowest possible integer result is 48

Melody  Jul 1, 2015
#6
+92
+3

wow, what would Capt. Man say now about poor Tommy getting an F on his last test?

he tried to be my dad for 3 days, and complained that I had a C+ in History

and Ms.Shapen always tries to put my history test score in front of my locker (which is an F obviously cuz im too busy with crime fighting, making my family chili meatballs, which are not spicy, and school homework and school tests, along with science projects)

KidDanger  Jul 1, 2015