SOLUTION: Fifi and Maxx together weigh 72 pounds Maxx and Sparky have a combined weight of 86 pounds Sparky and Fifi have a combined weight of 35 pounds So how much does each dog weigh?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Fifi and Maxx together weigh 72 pounds Maxx and Sparky have a combined weight of 86 pounds Sparky and Fifi have a combined weight of 35 pounds So how much does each dog weigh?      Log On


   

Question 115462: Fifi and Maxx together weigh 72 pounds
Maxx and Sparky have a combined weight of 86 pounds
Sparky and Fifi have a combined weight of 35 pounds
So how much does each dog weigh?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let Fifi weigh x_pounds
Maxx weigh y_pounds
and Sparky weigh z_pounds
Given:
Fifi and Maxx together weigh 72 pounds: then we have
x+%2B+y+=+72_pounds
Maxx and Sparky have a combined weight of 86 pounds: then we have
y+%2B+z+=+86_pounds

Sparky and Fifi have a combined weight of 35 pounds: then we have
x+%2B+z++=+35_pounds

Solve this system to find out how much does each dog weigh.
x+%2B+y+=+72_pounds…………………………….(1)
y+%2B+z++=+86_pounds…………………………….(2)
x+%2B+z++=+35_pounds+…………………………….(3)
Let subtract (3) from (2) to eliminate one unknown variable, variable z :
y+%2B+z+=+86_pounds…………………………….(2)….
-x+%2B+z+=+35_pounds…………………………….(3)
---------------------------------------
y+-x%2B+z-z+=+86_pounds+-+35_pounds+………
y+-x=+51_pounds…………………………………………………(4)

Let’s now add (1) and (4) to eliminate one unknown variable, variable x :
x+%2B+y+=+72_pounds…………………………….(1)
+y+-x=+51_pounds…………………………………………………(4)
----------------------------
x-x%2B+y+%2By+=+72_pounds+%2B+51_pounds+………

2+y+=+123_pounds
y+=+123_pounds%2F2
y+=+%2861.5%29_pounds……………………………………………(I)
Now use (1) and (II) to find out what x is equal to:
x+%2B+y+=+72_pounds…………………………….(1)
y+=+%2861.5%29_pounds+……………………………(I)….put the value of y in (1)
x+%2B+%2861.5%29_pounds+=+72_pounds…………………………….(1)
x+=+72_pounds+-+%2861.5%29_pounds+………

x+=+%2810.5%29_pounds+…………………………….(II)
Now find out what z is equal to: we can use
x+%2B+z++=+35_pounds+…………………………….(3) put the value of x from (II)
%2810.5%29_pounds+%2B+z++=+35_pounds+
+z++=+35_pounds+-+%2810.5%29_pounds+
+z++=+%2824.5%29_pounds++…………………………..(III)

our solutions are:
Fifi weigh x-+pounds+=+%2810.5%29_pounds
Maxx weigh y-+pounds+=+%2861.5%29_pounds
and Sparky weigh z-+pounds+=+%2824.5%29_pounds++

Check:
Fifi and Maxx together weigh 72+pounds: then we have
x+%2B+y+=+%2810.5%29_+pounds+%2B+%2861.5%29_pounds+=+72_+pounds
Maxx and Sparky have a combined weight of 86+pounds: then we have
y+%2B+z++=%2861.5%29_pounds+%2B++%2824.5%29_+pounds++=+86_pounds

Sparky and Fifi have a combined weight of 35 pounds: then we have
x+%2B+z++=+%2810.5%29_pounds+%2B++%2824.5%29_pounds++=+%2835%29_pounds+