The mean of n numbers is the sum of the numbers divided by n.
You have a mean score of 84 after taking 5 tests. Let x be the sum of scores.
You scored a total of 420 points on five tests.
You need to have a mean score of 85 after taking 6 tests. Let y be the score you need to obtain. Your total score on 6 tests is 420+y.
You need to score 90 points on the sixth test.
Answer:
Step-by-step explanation:
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Remark
Forget the Gamestop. I'd never use it. This one is on the house.
Solution
2.5(10 - x) + 10 = 72 - 1.5x*(5x + 12) The first step is to remove the brackets. Be very careful you understand the bracket on the right.
25 - 2.5x + 10 = 72 - 7.5x - 18 Study the signs carefully. Collect like terms.
35 - 2.5x = 54 - 7.5x Add 7.5x to both sides.
35 - 2.5x + 7.5x = 54 - 7.5x + 7.5x
35 + 5x = 54 Subtract 35 from both sides.
5x = 19 Divide by 5
x = 19/5
x = 3 4/5 = 3.8
Check
When you numbers are so cumbersome, you should check the answer.
<em><u>LHS</u></em>
2.5(10 - 3.8) + 10
2.5(6.2) + 10
15.5 + 10
25.5
<em><u>RHS</u></em>
72 - 1.5(5*3.8 +12)
72 - 1.5(19 + 12)
72 - 1.5(31)
72 - 46.5
25.5
<em><u>RHS = LHS</u></em> The solution checks.
488 cm squared is the total area
Let the width be "x" cm.
Then the length is "x+12" cm
And the area = x(x+12) = x^2+12x cm^2
----------------------------
Change the dimensions:
width = "x-2" cm
length = "x+10" cm
New area = (x-2)(x+10) = x^2 + 8x - 20 cm^2
------------------
Equations :
Old area - New area = 108 cm^2
x^2+12x -(x^2 + 8x - 20) = 108
4x + 20 = 108
4x = 88
x = 22 cm (original width)
x+12 = 24 cm (original length)
