Problema Solution

Louisa and Kayla had $300. After Luisa had spent $112 and Kayla spent $40, 2/5 of Luisa's remainder is equal to 5/6 of Kayla's remainder. How much did Luisa have at first?

Answer provided by our tutors

Let

x = the amount that Luisa had at first, x>=0

y = the amount that Kayla had at first, y>=0

Together they had $300:

x + y = 300

y = 300 - x

After Luisa spent $112 she has: x - 112 left

After Kayla spent $40 she has: y - 40 left

(2/5) of (x - 112) equals (5/6) of (y - 40) or:

(2/5)(x - 112) = (5/6)(y - 40)

Plug y = 300 - x into (2/5)(x - 112) = (5/6)(y - 40):

(2/5)(x - 112) = (5/6)((300 - x) - 40)

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click here to see the equation solved for x

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x = $212

At the beginning, Luisa had $212.