Question 1167914
Bill's sweets at start = x
Ben's sweets at start = y
<pr>
2/7(x) = 2/3(y)
y - 120 = 1/4(2/7(x))
<pr>
Simplify equations:
<pr>
2/7(x) = 2/3(y)
y - 120 = 1/14(x)
<pr>
2/7(x) - 2/3(y) = 0
-1/14(x) + y = 120
<pr>
Multiply second equation by 2/3:
<pr>
2/7(x) - 2/3(y) = 0
-1/21(x) + 2/3(y) = 80
<pr>
Add both equations together:
<pr>
5/21(x) = 80
<pr>
Solve for x:
<pr>
x = 80(21/5)
<pr>
x = 336
<pr>
Now that we know x = 336, we can plug this into any previous equation to find out what y equals.
<pr>
2/7(x) = 2/3(y)
<pr>
2/7(336) = 2/3(y)
<pr>
96 = 2/3(y)
<pr>
y = 96(3/2)
<pr>
y = 144
<pr>
Bill's sweets at start = x = <b>336</b>
Ben's sweets at start = y = <b>144</b>