matching match boxes and match sticks

Algebra Level 1

I have unknown numbers of matchboxes and matchsticks.

  • If I put 12 sticks in each box, 2 sticks are left and 2 boxes are left empty.
  • If I put 7 sticks in each box, 8 sticks are left.

Find the sum of the number of matchboxes and the number of matchsticks that I have.


The answer is 56.

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1 solution

Let b b be the number of match boxes that I have and s s be the number of match sticks that I have. Then

s b 2 = 12 + 2 b 2 \dfrac{s}{b-2}=12+\dfrac{2}{b-2} ( 1 ) \color{#D61F06}(1)

s b = 7 + 8 b \dfrac{s}{b}=7+\dfrac{8}{b} ( 2 ) \color{#D61F06}(2)

Solving the system of equations gives b = 6 b=6 and s = 50 s=50 . The desired answer is 6 + 50 = 56 6+50=56 .

um i dont understand hlep

Kevin Tacheny - 2 years, 5 months ago

help not hlep

Kevin Tacheny - 2 years, 5 months ago

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