SOLUTION: Four friends bought a boat for $1200. Friend A paid half the sum of the amounts paid by the other 3 friends. Friend B paid one-third the sum paid by the other three. Friend C paid

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Question 1050566: Four friends bought a boat for $1200. Friend A paid half the sum of the amounts paid by the other 3 friends. Friend B paid one-third the sum paid by the other three. Friend C paid one-fourth the sum paid by the other three. Friend D paid the rest. How much did friend D pay?
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!






Your choice of methods may be Substitution, Elimination, or Matrix Row Reduction operations. I stop here unless you need further help. (Assuming your course is Algebra 1).
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Four friends bought a boat for $1200. Friend A paid half the sum of the amounts paid by the other 3 friends.
Friend B paid one-third the sum paid by the other three. Friend C paid one-fourth the sum paid by the other three.
Friend D paid the rest. How much did friend D pay?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

From the condition, you have this system of 4 equations

a + b + c + d = 1200,
a = ,
b = ,
c = 


You can rewrite it in this form

a + b + c + d = 1200,   (1)
    b + c + d = 2a,     (2)
a +     c + d = 3b,     (3)
a + b +     d = 4d.     (4)


Now I will show you how to find the solution easily.


Distract equation (2) from equation (1) (both sides). You will get 

a = 1200 - 2a  --->  3a = 1200  --->  a =  = 400.


Distract equation (3) from equation (1) (both sides). You will get 

b = 1200 - 3b  --->  4b = 1200  --->  b =  = 300.


Distract equation (4) from equation (1) (both sides). You will get 

c = 1200 - 4c  --->  5c = 1200  --->  c =  = 240.

Now from (1) you have for d:  d = 1200 - a - b - c = 1200 - 400 - 300 - 240 = 260.


Answer.  D payed $260.


Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Four friends bought a boat for $1200. Friend A paid half the sum of the amounts paid by the other 3 friends. Friend B paid one-third the sum paid by the other three. Friend C paid one-fourth the sum paid by the other three. Friend D paid the rest. How much did friend D pay?
A + B + C + D = 1,200 ------- eq (i)

_________2A = B + C + D_____2A - B - C - D = 0 ------- eq (ii)

___________3B = A + C + D____A - 3B + C + D = 0 ------ eq (iii)

________4C = A + B + D____A + B - 4C + D = 0 --------- eq (iv)



3A = 1,200 ------- Subtracting eq (ii) from eq (i)

A paid:  = 



4B = 1,200 ------- Subtracting eq (iii) from eq (i)

B paid:  = 



5C = 1,200 ------- Subtracting eq (iv) from eq (i)

C paid:  = 

D paid: $1,200 - (400 + 300 + 240), or $1.200 - 940 =  

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