MATH
Solving Problems Involving System of Linear Equations
(Investment problems)

Ex.
Two investments are made totaling P15 000.Part of the P15 000 is invested at 9% and part at 10%.For a certain year,these investmentsyield P1 432 in simple interest.Find the amount invested to each rate.

let a=1st investment at 9%
b=2nd investment at 10%

(equation 1) (a+b=15 000 )-0.1
(equation 2) 0.09a+0.16=1432

0.09a+0.16=1432
-o.19+0.16=-1 5 000
_______________
-0.01a/0.01 =-168/0.01
a =P 6 800

b=15 000 - a
b=15 000 -6800
d=P8 200

9%=P6 800
10%=P8 200

Solving Problems Involving System of Linear Equations
(Mixture problems)

Ex.
One canned juice drink is 15% lemon juice;another is 5% lemon juice.How many liter of each should be mixed together in order to get 10L that is 10% lemon juice.

(equation1) x+y=10L
15%(x)+5%(y)=10L(10)
(equation2) 0.15x+0.05y=10(0.1)

o.15x+o.o5(10-x)=1
o.15+0.5-0.05 =1 (transpose 0.5 to the other side)
0.1x/ 0.1 =0.5/0.1
x = 5
15% lemon juice=5L
5% lemon juice=5L