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):
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).
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?
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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.
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 =
(