So far this year Nick has scored a 75, 81, 88 and 92 on four of his math tests. Each test is worth a maximum of 100 points.
To earn a B this year, Nick needs a test average of 80 or better.
Write the inequality that represents this scenario. Let t equal Nick's grade on the fifth and the last test.
___+ t ≥ ___
336 + t ≥ 400
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t1 = 75 = results of the first test
t2 = 81 = results of the secondt test
t3 = 88 = results of the third test
t4 = 92 = results of the fourth test
t = results of the fifth test
average of 5 test
a = ( t1 + t2 + t3 + t4 + t ) / 5
Nick needs a test average of 80 or better mean:
( t1 + t2 + t3 + t4 + t ) / 5 ≥ 80
( 75 + 81 + 88 + 92 + t ) / 5 ≥ 80
( 336 + x ) / 5 ≥ 80 Multiply both sides by 5
336 + t ≥ 80 * 5
336 + t ≥ 400 Subtract 336 to both sides
336 + t - 336 ≥ 400 - 336
t ≥ 64
Proof:
( t1 + t2 + t3 + t4 + t ) / 5
=
( 75 + 81 + 88 + 92 + 64 ) / 5 =
400 / 5 = 80
To find the inequality that represents Nick's scenario, we need to calculate his test average and compare it to the required average for a B.
The test average is calculated by summing up all the test scores and dividing by the total number of tests. In this case, Nick has taken 4 tests so far, and the sum of his scores is 75 + 81 + 88 + 92 = 336.
To calculate the test average, divide the sum of the scores by the number of tests: 336 / 4 = 84.
Now, since Nick needs a test average of 80 or better to earn a B, the inequality will be:
84 + t ≥ 80
This inequality states that the sum of Nick's average (84) and his score on the fifth test (t) must be greater than or equal to 80 in order to earn a B.