money question

Question

Together Evan, Katie, and McKenna had $865 when they left to go shopping. Evan spent 2/5 of his money. Katie spent $40. McKenna spent twice as much as Evan. McKenna spent twice as much as Evan,They each have the same amount of money left. How much money did each of them originally take shoppin?

Answer 1

Hmmm, so here's where I would start.  I would create equations for each of this pieces of information given you, in terms you can understand.  I would use E = Evan's starting money, K = Katie's, and M = Mckenna's.  And since they all have the same amount left we can say L = money left over in each of their hands.

 

So fist, E + K + M = 865 (they had 865 when they went shopping)

 

E - 2/5 * E = L (Evan spent 2/5 of his money)

 

K - 40 = L (Katie spent $40)

 

M - 2(2/5*E) = L (Mckenna spent twice as much as Evan)

 

This is great for us because we have 4 equations and we have 4 variables.  That's all we need to find the right answer.  Let's reformat a little bit.

 

E = 5/3 * L

 

K = L + 40

 

M = L + 4/5 * E or better yet, M = L + 4/5 * (5/3 * L) = L + 4/3*L = 7/3 * L

 

then,

 

5/3*L + L + 40 + 7/3*L = 865

 

5L + 40 = 865

 

5L = 825

 

L = 165

 

So, what they each have left is 165.  Plugging this back into their original equations.  Evan started with 275.  Katie started with 205.  McKenna started with 385.  Just to check ourselves, we'll add those back and make sure they equal 865.  And they do, so we're good.  And we know that McKenna is the rich one.