Question #2648

Jacob has 100 sports cards. He has football, basketball, and baseball cards. Use these clues to find out how many of each type he owns.

He has three time as many football cards as basketball cards.

He has 10 more basketball cards than baseball cards.

He has three time as many football cards as basketball cards.

He has 10 more basketball cards than baseball cards.

Expert's answer

Denote football cards as Fb, basketball cards as Bk, baseball cards as Bs. Let's construct the system of equations:

Fb + Bk + Bs = 100

Fb = 3Bk

Bk = Bs + 10

Fb = 3(Bs + 10)

3(Bs + 10) + Bs + 10 + Bs = 100

5Bs = 100 - 40 = 60

Bs = 12,& Bk = 12+10 = 22,& Fb = 22*3 = 66.

Fb + Bk + Bs = 100

Fb = 3Bk

Bk = Bs + 10

Fb = 3(Bs + 10)

3(Bs + 10) + Bs + 10 + Bs = 100

5Bs = 100 - 40 = 60

Bs = 12,& Bk = 12+10 = 22,& Fb = 22*3 = 66.

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