Challenging word problem.

Question

Trying to help my daughter with her 4th grade math!!!

 

Two-thirds of Mr. Hussein's money is equal to 3/5 of Ms. Lee's money Ms. Lee has $20 more than Mr. Hussein. How much money do they have altogether?

Answer 1

Let H = Mr. Hussein's money

Let L = Ms. Lee's money

 

L = H + 20, since Ms. Lee has $20 more than Mr. Hussein

 

(2/3)*H = (3/5)*L since two-thirds of Mr. Hussein's money is equal to 3/5 of Ms. Lee's money

 

First I would simplify the 2nd equation by multiplying each side by 3 to get

 

2*H = (9/5)*L

 

Then I would multiply this equation by 5 to get

 

10*H = 9*L

 

Now I would substitute the value of L from the 1st equation ( L = H + 20 ) into this new equation

 

10*H = 9*(H+20)

10*H = 9*H + 180

H = 180

 

so L = 180 + 20 = 200

 

So together they have 180 + 200 = $380

 

Check: L = 200, H = 180 so L = H + 20

Check:  (2/3) * H = (2/3) * 180 = 120

            (3/5) * L = (3/5) * 200 = 120,  so (2/3)*H = (3/5)*L