# Project 1

### Project 1

MC
##### Marian Carbonel
Marian's Personal Gallery
##### Transcript
00:04
Rational Function
00:06
in Real Life
00:07
Presented by:
00:08
John Peter B. Carbonel
00:13
What is Rational Function?
00:16
- is any function that can be defined by a rational fraction.
00:21
- numerator and denominator are polynomials
00:28
f(x) = P(x)/Q(x)
00:28
P(x) and Q(x) are Polynomials, and Q(x) is not equal to 0
00:28
where,
00:36
Sample Problem
00:38
Elyn bought 85 kilograms of fruits consisting of Dalandan and Mango for her fruit stand business. She bought P1320 worth of dalandan and P3120 worth of Mango. If the cost per kilogram of mango is P20 more than that of dalandan, how many kilograms of each fruit did she buy?
00:60
Step 1
01:01
x = kilograms of Dalandan
01:03
85-x = kilograms of Mango
01:06
Step 2
01:08
no. of kg bought
01:08
cost per kg
01:08
Total Cost
01:08
Mango
01:08
1320
01:08
Dalandan
01:10
x
01:10
1320/x
01:11
3120
01:12
85-x
01:13
3120/80-x
01:17
Step 3
01:18
Cost per kg of mango               = P20 + cost/kg of dalandan
01:20
3120 85-x
01:22
=   20 +
01:23
1320    x
01:28
1320    x
01:28
=              +
01:28
20   1
01:28
3120 85-x
01:30
3120 85-x
01:31
01:32
20x + 1320         x
01:37
Step 4
01:38
20x + 1320         x
01:38
01:38
3120 85-x
01:44
LCD
01:45
x (85 - x)
01:53
Step 5
01:54
(x) (85x)
01:55
( )
01:55
3120 85-x
01:58
01:58
(           )
01:58
20x + 1320         x
01:60
(x) (85x)
02:04
3120x = (20x + 1320)(85-x)
02:06
3120x = (20x + 1320)(85-x)
02:09
3120x = 1700x - 20x + 112,200 - 1320x
02:11
2
02:12
3120x = 20x  +1700x - 1320x + 112,200
02:14
2
02:16
3120x = -20x  + 380x + 112,200
02:18
2
02:19
20x  + 3120x - 380x - 112,200 = 0
02:20
2
02:23
20x  + 2740x - 112,200                     20
02:24
2
02:27
= 0
02:28
x  + 137x - 5610 = 0
02:29
2
02:31
02:36
a=1 b=137 c=-5610
02:39
There are 33kg of Dalandan that Elyn bought.
02:41
Step 6
02:42
3120 85-x
02:44
=  20 +
02:44
1320     x
02:45
3120 85-x
02:46
= 20 +
02:46
1320 x
02:47
60 = 60
02:48
x = 33 -> no. of Dalandan
02:49
85 - x
02:50
85 - 33 = 52
02:51
Elyn bought 85kg of Fruits