The Triangular Caf e ˊ serves 4 different main dishes, 3 different sides, and 3 different desserts. The M o ¨ bius Strip Grill serves 4 different main dishes, 1 side, and 3 different desserts. If a meal consists of 1 main dish, 1 side, and 1 dessert, how many more different meals are possible at the Triangular Caf e ˊ than the M o ¨ bius Strip Grill?
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At both the Triangular Caf e ˊ and the M o ¨ bius Strip Grill, there are 4 main dishes and 3 desserts. In order to find the total number of possibilities, we multiply, so there are 4 ⋅ 3 = 1 2 main dish-dessert combinations. The Triangular Caf e ˊ has 2 more sides than the M o ¨ bius Strip Grill, so the total number of meals is 1 2 ⋅ 2 = 2 4 greater than that of the M o ¨ bius Strip Grill. Alternately, we find the number of meals at each restaurant and then subtract. This yields ( 4 ⋅ 3 ⋅ 3 ) − ( 4 ⋅ 1 ⋅ 3 ) = 3 6 − 1 2 = 2 4 more meals at the Triangular Caf e ˊ .
P.S. If any of you know how to format the e ˊ or o ¨ without having to put it into L a T e X style, could you please tell me how so it doesn't look weird with the rest of the text? Thanks!
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At the Triangular Cafe:
4 different main dishes, 3 different sides and 3 different desserts
By rule of product , the number of meals is 4 ( 3 ) ( 3 ) = 3 6
At the Mobius Strip Grill:
4 different main dishes, 1 side and 3 different desserts
By rule of product , the number of meals is 4 ( 1 ) ( 3 ) = 1 2
Finally, the difference is
3 6 − 1 2 = 2 4 m e a l s