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?
+427 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
+129852 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
+118673 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
$$\\81.5\le \frac{360+fourth}{5}<82.5\\\\
407.5\le 360+fourth<412.5\\\\
47.5\le fourth<52.5\\\\
$But all the scores were integers so$\\\\
$the lowest possible score for the fourth test was $ 48$$
+118673 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
+92 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)
