The number of Roberto's baseball cards is 3/4 the number of David's cards. If Roberto gives 1/2 of his cards to David, What will be the ratio of Roberto's cards to David's cards?
The ratio of Roberto's cards to Davids cards is 3:4. After giving half his cards, the ratio becomes 3 - 3/2 to 4 + 3/2, or 3/2 to 11/2, so the ratio now becomes 3:11. ☺☺☺☺
r/d = 3/4
(r/2)/(d+r/2)
= r/(2d+r)
= 1/((2d+r)/r)
= 1/(2d/r + 1)
= 1/(2(4/3)+1)
= 1/(11/3)
= 3/11
To find the ratio of Roberto's cards to David's cards after Roberto gives some to David, let's break down the problem step by step.
Step 1: Let's assume David has "x" number of cards.
Step 2: According to the given information, Roberto's number of cards is 3/4 times the number of David's cards, which can be expressed as (3/4) * x.
Step 3: Now, if Roberto gives away 1/2 of his cards to David, he will be left with (1 - 1/2) = 1/2 of his original number of cards.
Step 4: Therefore, if Roberto originally had (3/4) * x cards and he gives away 1/2 of them, his new number of cards will be (1/2) * (3/4) * x.
Step 5: Simplifying the above expression, we get (3/8) * x as the number of Roberto's cards after giving away some to David.
Step 6: The number of David's cards after receiving from Roberto will be x + [(1/2) * (3/4) * x] = x + (3/8) * x = (8/8 + 3/8) * x = (11/8) * x.
Step 7: Now we have the number of Roberto's cards as (3/8) * x and the number of David's cards as (11/8) * x, which gives us the ratio of Roberto's cards to David's cards as (3/8) * x : (11/8) * x.
Step 8: Canceling out the common factor of "x" in the above ratio, we find the final ratio of Roberto's cards to David's cards as 3/8 : 11/8.
Step 9: To simplify this ratio further, we can multiply both numerator and denominator by 8, giving us the ratio 24 : 11.
Therefore, the ratio of Roberto's cards to David's cards after Roberto gives away 1/2 of his cards will be 24 : 11.