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Question 983046: please help me to solve Al,Bill and Carl went shopping.When they compared the totals that each had spent they found that: Al and Bill together spent a total of Php 1 200; Bill and Carl together spent a total of Php 1 800.00; and Al and Carl together spent a total of Php 1 000.How much did each person spend?
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Al,Bill and Carl went shopping.
When they compared the totals that each had spent they found that:
Al and Bill together spent a total of Php 1200;
a + b = 1200
Bill and Carl together spent a total of Php 1800.00;
b + c = 1800
and Al and Carl together spent a total of Php 1000.
a + c = 1000
How much did each person spend?
:
use elimination on the 1st two equations
0 + b + c = 1800
a + b + 0 = 1200
-------------------Subtraction eliminates b
-a + 0 + c = 600
c = (a+600)
In the 3rd equation; a + c = 1000, replace c with (a+600)
a + (a+600) = 1000
2a = 1000 - 600
2a = 400
a = 400/2
a = 200
find c using equation c = a + 600
c = 200 + 600
c = 800
Find b using the 2nd equation, replace c with 800
b + 800 = 1800
b = 1800 - 800
b = 1000
:
We have:
Al spent 200
Bill spent 1000
Carl spent 800
:
you can check and see if all this adds up
Answer by ikleyn(52775)  (Show Source):
You can put this solution on YOUR website!
Let a be the amount that Al spent (in Php);
b be the amount that Bill spent (in Php), and
c be the amount that Carl spent (in Php).
Then you have 3 equations in 3 unknowns:
a + b = 1200, (1)
b + c = 1800, (2)
a + c = 1000. (3)
Add all three equations (which means "add their left sides and add their right sides"). You will get
2*(a + b + c) = 1200 + 1800 + 1000 = 4000, or
a + b + c = 2000. (4)
Now, distract the equation (1) from (4). You will get
c = 2000 - 1200 = 800. Hence, Carl spent 800 Php.
Next, distract the equation (2) from (4). You will get
a = 2000 - 1800 = 200. Hence, Al spent 200 Php.
Finally, distract the equation (3) from (4). You will get
b = 2000 - 1000 = 1000. Hence, Bill spent 1000 Php.
Answer. Al spent 200 Php, Bill spent 1000 Php, and Carl spent 800 Php.
For more similar problems see the lesson The tricks to solve some word problems with three and more unknowns using mental math in this site.
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