The number of tim's stamps is 3/4 the number of david's stamps.if tim gives 1/2 of his stamps to david,what will be the ratio of the number of tim's stamps to the number of david's stamps?
Number of stamps for david -- 4 x
number of stamps for Tim = 3x
after give-away,
Tim has 1.5x
David has 5.5x
ratio of Tim : David
= 1.5x : 5.5x
= 1.5 : 5.5
= 15 : 55
= 3 : 11
To find the ratio of the number of Tim's stamps to the number of David's stamps, we first need to determine their initial quantities.
Let's assume that Tim has x stamps. According to the given information, David would then have 4/3 times the number of Tim's stamps, which is (4/3)x stamps.
If Tim gives 1/2 of his stamps to David, he would be left with 1/2*x stamps, which simplifies to x/2 stamps.
David would receive these stamps, and his new total would be:
(4/3)x + x/2
To find the common denominator, we multiply 3 and 2, resulting in:
(8/6)x + (3/6)x
Combining the terms, we have:
(11/6)x
So, David now has (11/6)x stamps.
The ratio of the number of Tim's stamps to the number of David's stamps is therefore:
(x/2) : (11/6)x
To simplify this ratio, we can multiply both sides by 6:
6*(x/2) : 6*(11/6)x
Which simplifies to:
3x : 11x
Therefore, the ratio of the number of Tim's stamps to the number of David's stamps would be 3x : 11x.