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The magician Moolin can make two different spells: Thunder— two vials of dragon tears and five vials of liquid pearl. Lightning— three vials of dragon tears and two vials of liquid pearl. Moolin has vials of dragon tears and liquid pearl at a ratio of 4 to 5. If Moolin wants to use up all of its ingredients, what ratio of Thunder to Lightning should he make? Please give the answer as a fraction in the simplest term (e.g. if the ratio is 2:3, write 23).

 Jan 9, 2021
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The magician Moolin can make two different spells: Thunder— two vials of dragon tears and five vials of liquid pearl. Lightning— three vials of dragon tears and two vials of liquid pearl. Moolin has vials of dragon tears and liquid pearl at a ratio of 4 to 5. If Moolin wants to use up all of its ingredients, what ratio of Thunder to Lightning should he make? Please give the answer as a fraction in the simplest term (e.g. if the ratio is 2:3, write 23).

 

Thunder requires  2A  Dragon tears and  3A liquid pearls

Lighting  requires  3B Dragon tears and  2B liquid pearls

 

Moonshine   has   4X  Dragon tears and  5X   liquid pearls

 

so

2A + 3B = 4X

3A + 2B = 5X

 

solve simultaneously and get all values in terms of just one.

Then look at the required ratio.

 Jan 10, 2021
edited by Melody  Jan 10, 2021

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