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?
<pre>A + B + C + D = 1,200 ------- eq (i)
{{{A = (1/2) * (B + C + D)}}}_____{{{A = (B + C + D)/2}}}____2A = B + C + D_____2A - B - C - D = 0 ------- eq (ii)
{{{B = (1/3) * (A + C + D)}}}_____{{{B = (A + C + D)/3}}}______3B = A + C + D____A - 3B + C + D = 0 ------ eq (iii)
{{{C = (1/4) * (A + B + D)}}}____{{{C = (A + B + D)/4}}}____4C = A + B + D____A + B - 4C + D = 0 --------- eq (iv)

3A = 1,200 ------- Subtracting eq (ii) from eq (i)
A paid: {{{"$1,200"/3}}} = {{{highlight_green("$400")}}}

4B = 1,200 ------- Subtracting eq (iii) from eq (i)
B paid: {{{"$1,200"/4}}} = {{{highlight_green("$300")}}}

5C = 1,200 ------- Subtracting eq (iv) from eq (i)
C paid: {{{"$1,200"/5}}} = {{{highlight_green("$240")}}}
D paid: $1,200 - (400 + 300 + 240), or $1.200 - 940 = {{{highlight_green("$260")}}}