SOLUTION: Translate into algebraic equations : 1- A student averages 84 on five tests. If the student received grades of 84, 82, 81, and 79 on the first four exams, what grade did the st

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Question 134990: Translate into algebraic equations :
1- A student averages 84 on five tests. If the student received grades of 84, 82, 81, and 79 on the first four exams, what grade did the student receive on the fifth exam?
2-The area of a rectangle is 45 square cm. If the length is 4 cm greater than the width, what are the dimension of the rectangle?
3- Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. How much time did each require?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1- A student averages 84 on five tests. If the student received grades of 84,
82, 81, and 79 on the first four exams, what grade did the student receive on
the fifth exam?
:
Let x = the grade of the fifth exam
:
%28%2884%2B82%2B81%2B79%2Bx%29%29%2F5 = 84
%28%28326%2Bx%29%29%2F5 = 84
Multiply equation by 5 to get rid of the denominator
326 + x = 420
:
x = 420 - 326
:
x = 94 is the grade he made on the 5th test
:
Check on a calc: enter (84+82+81+79+94)/5
:
:
2-The area of a rectangle is 45 square cm. If the length is 4 cm greater than
the width, what are the dimension of the rectangle?
:
Let x = width
then
(x+4) = length
:
Using the area formula:
x(x+4) = 45
x^2 + 4x - 45 = 0; arrange as a quadratic equation
Factor
(x+9)(x-5) = 0
Positive solution
x = 5 cm is the width
then
5+4 = 9 cm is the length
:
;
3- Lydia takes ten minutes more to complete an illustration than Tom.
The total time taken by both of them is six hours. How much time did each require?
:
It may to easier to deal with this in minutes: Convert 6 hrs to 360 min
:
Let t = time (in min)required by Tom by himself
then
(t+10) = time required by Lydia by herself
:
Let the completed job = 1
:
360%2Ft + 360%2F%28%28t%2B10%29%29 = 1
:
Multiply equation by t(t+10), resulting in:
360(t+10) + 360t = t(t+10)
:
360t + 3600 + 360t = t^2 + 10t
:
720t + 3600 = t^2 + 10t
Arrange as a quadratic equation
t^2 + 10t - 720t - 3600 = 0
:
t^2 - 710t - 3600 = 0
Use the quadratic formula for this: a=1; b=-710; c=-3600
:
You should get a solution of t ~ 715 minutes
:
Tom's time by himself = 11 hrs 55 min
Lydia's time by herself = 12 hr 5 min
:
Check this solution:
360%2F715 + 360%2F725 =
.5035 + .4965 = 1.00;