Find the number of each kind of object in the collection.
Sue's Card Collection
8 packs of baseball cards
3 fewer packs of hockey cards than football cards
17 packs in all
8 + f + f-3 = 17
2f = 12
f = 6
6 packs of football cards
To find the number of each kind of object in Sue's card collection, we can use algebra to solve the problem.
Let's denote the number of packs of baseball cards as "B", the number of packs of hockey cards as "H", and the number of packs of football cards as "F".
From the given information, we know the following:
- 8 packs of baseball cards: B = 8
- 3 fewer packs of hockey cards than football cards: H = F - 3
- 17 packs in total: B + H + F = 17
To find the values of B, H, and F, we need to solve these equations simultaneously. Here's how:
1. Substitute the given value for B (8) into the third equation:
8 + H + F = 17
2. Substitute the value of H from the second equation (H = F - 3) into the substituted equation:
8 + (F - 3) + F = 17
3. Simplify the equation:
8 + F - 3 + F = 17
2F + 5 = 17
4. Subtract 5 from both sides of the equation:
2F = 12
5. Divide both sides by 2:
F = 6
Now that we have the value of F, we can substitute it back into the second equation to find H:
H = 6 - 3
H = 3
Thus, Sue has 8 packs of baseball cards, 3 packs of hockey cards, and 6 packs of football cards in her collection.