The ratio of Peter's marbles to the number of Harry's marbles was 4:5. After Harry gave away 8 marbles and Peter bought another 11 marbles, Harry had as many marbles as Peter. How many marbles did Peter have at first?
+33659 Peter's marbles initially = p
Harry's marbles initially = h
p/h = 4/5
p+11 = h - 8
From the first equation p = 4h/5. Put this into the second
4h/5 + 11 = h - 8 Subtract 4h/5 from both sides and add 8 to both sides
19 = h/5 Multiply both sides by 5
h = 95 Put this into p = 4h/5 to get
p = 4*95/5 or p = 76
Peter had 76 marbles at first.
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+33659 Peter's marbles initially = p
Harry's marbles initially = h
p/h = 4/5
p+11 = h - 8
From the first equation p = 4h/5. Put this into the second
4h/5 + 11 = h - 8 Subtract 4h/5 from both sides and add 8 to both sides
19 = h/5 Multiply both sides by 5
h = 95 Put this into p = 4h/5 to get
p = 4*95/5 or p = 76
Peter had 76 marbles at first.
.
+129850 Call the number of marbles that Harry had, x........so, Peter had (4/5)x
So
x - 8 = (4/5)x + 11 add 8 to both sides, subtract (4/5)x from both sides
(1/5)x = 19 multiply both sides by 5
x = 95 = the number of marbles that Harry had, at first
And Peter had (4/5)x = (4/5)*95 = 76
Proof.....
Harry started with 95 and gave away 8 = 87
Peter started with 76 and received 11 = 87
