SOLUTION: Hi If A gave 22 sweets to D she would have 4 times as many sweets as D . If D gave 18 sweets to A she would have 1/9 as many sweets as A and D. How many sweets do they have altog

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Question 1177321: Hi
If A gave 22 sweets to D she would have 4 times as many sweets as D . If D gave 18 sweets to A she would have 1/9 as many sweets as A and D.
How many sweets do they have altogether.
Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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If A gave 22 sweets to D she would have 4 times as many sweets as D.
a - 22 = 4(d+22)
a - 22 = 4d + 88
a - 4d = 22 + 88
a - 4d = 110
If D gave 18 sweets to A she would have 1/9 as many sweets as A and D.
d - 18 = 1%2F9(a+d), total remain the same
mult the eq by 9, cancel the denominator
9d - 162 = a + d
-a + 9d - d = 162
-a + 8d = 162
:
Use these two equations for elimination
a - 4d = 110
-a +8d = 162
-------------------addition eliminates a, find d
0 + 4d = 272
d = 272/4
d = 68 sweets for D originally
then
a - 22 = 4(68+22)
a = 4(90) + 22
a = 360 + 22
a = 382 sweets for A originally
:
How many sweets do they have altogether.
382 + 68 = 450