The ratio of Doug's sports cards to Philip's sports cards was 7:5. When Doug gave 3 sports cards to Philip, they each had the same amount. How many sports cards did they have altogether?
Ratio of Doug’s sports cards to Philip’s sports cards: 7 + 5 = 12
Doug gives Philip 3 sports cards: 12 * 3 = 36
They have 36 sports cards altogether
7 * 3 = 21
5 * 3 = 15
21 + 15 = 36
36 sports cards
algebraic solution:
Doug had 7x and Phil had 5x
after the gifting:
Doug had 7x-3 , Phil had 5x+3
now they have the same, so
7x - 3 = 6x + 3
x = 6
total is 7x+5x = 12x = 12(6) = 36
To solve this problem, we can start by setting up a system of equations based on the given information.
Let's assume that Doug initially had 7x sports cards and Philip had 5x sports cards. Since the ratio of their cards is 7:5, Doug's cards would amount to 7 times some value x, and Philip's cards would be 5 times the same value x.
After Doug gave 3 sports cards to Philip, we know that they both had the same amount of cards. Let's consider their new card totals:
Doug: 7x - 3
Philip: 5x + 3
Now we can set up an equation based on their new card totals:
7x - 3 = 5x + 3
To solve for x, we can simplify the equation:
7x - 5x = 3 + 3
2x = 6
Dividing both sides of the equation by 2, we find:
x = 3
Now we can substitute the value of x back into the initial equations to find the number of sports cards each person has:
Doug: 7x = 7 * 3 = 21 sports cards
Philip: 5x = 5 * 3 = 15 sports cards
Finally, to find the total number of sports cards they have altogether:
Total = Doug's cards + Philip's cards
Total = 21 + 15
Total = 36
Therefore, Doug and Philip have a total of 36 sports cards altogether.