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
To find the number of each kind of object in Sue's card collection, we can use a system of linear equations.
Let's define:
x = the number of packs of baseball cards
y = the number of packs of football cards
z = the number of packs of hockey cards
From the given information, we know that:
x + y + z = 17 (equation 1)
x + z = 8 (equation 2)
z = y - 3 (equation 3)
First, let's solve equations 2 and 3 to find the relationship between the number of hockey cards and the number of football cards.
Substituting equation 3 into equation 2, we have:
x + (y - 3) = 8
x + y - 3 = 8
x + y = 11 (equation 4)
Now, let's solve equations 1 and 4 to find the values of x, y, and z.
Solving equations 1 and 4 simultaneously, we can eliminate the variable y.
Subtract equation 4 from equation 1:
(x + y + z) - (x + y) = 17 - 11
z = 6
Now, we can substitute z = 6 back into equation 2 to find the value of x:
x + 6 = 8
x = 8 - 6
x = 2
Finally, substitute x = 2 into equation 4 to find the value of y:
2 + y = 11
y = 11 - 2
y = 9
Therefore, the number of each kind of object in Sue's card collection is:
Baseball cards: 2 packs
Football cards: 9 packs
Hockey cards: 6 packs.
B + H + F = 17
B = 8
H = F - 3
Substitue into the original equation:
8 + F - 3 + F = 17
can you find F?
F= 6
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