SOLUTION: Emma decided to invest Php 120,000 in an internet café and a photo booth. The internet café and the photo booth pay monthly interest 5% and 4.5%,respectively. If she wants to

Question 1188262: Emma decided to invest Php 120,000 in an internet café and a photo booth. The internet
café and the photo booth pay monthly interest 5% and 4.5%,respectively. If she wants to
earn a total of Php 5,800 a monthly from the two businesses, how much must she allot to each business?
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = the amount invested at 5%.
y = the amount invested at 4.5%.

you have two equations that need to be solved simultaneously.
they are:

x + y = 120000
.05x + .045y = 5800

multiply both sides of the first equation by .05 and leave the second equation as is to get:

.05x + .05y = 6000
.05x + .045y = 5800

subtract the second equation from the first to get:

.005y = 200

solve for y to get:

y = 200 / .005 = 40000

since x + y = 120000, then x = 80000.

your solution is that she needs to invest 80000 in the internet cafe and 40000 in the photo booth.

confirm by replacing x and y in the original equation with 80000 and 40000.

you get:

x + y = 80000 + 400090 = 120000
.05x + .045y = .05*80000 + .045*40000 = 5800.

your solution is confirmed to be good.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Here is a quick and easy informal method for solving "mixture" problems like this, if a formal algebraic solution is not required.

(1) All 120,000 invested at 5% would yield 6000 interest; all invested at 4.5% would yield 5400 interest; the desired interest is 5800.
(2) Look at the three interest amounts 5400, 5800, and 6000 on a number line and observe/calculate that 5800 is 2/3 of the way from 5400 to 6000.
(3) That means 2/3 of the 120000 should be invested at the higher rate.

ANSWER: 2/3 of Php 120000, or Php 80000, at 5%; the other Php 40000 at 4.5%.

CHECK: .05(80000)+.045(40000) = 4000+1800 = 5800

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