# math

If I give you \$40 then the ratio of my money to yours is 4 : 5. On

the other hand, if you give me \$40, then the ratio is 8 : 1. How

much money do both of us have? please show all steps

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1. 4:5 = 40:50

8:1 = 80:10

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Ms. Sue
2. Let the money you have be "x" and what your friend has be "y."

In first case,

x:(y+40) = 4:5
5x = 4(y+40)
5x = 4y + 160
x = (4y+160)/5 ----- equation (i)

In second case,

(x+40):y = 8:1
x+40 = 8y
x = 9y-40
(4y+160)/5 = 8y-40 [from equation (i)]
4y+160 = 40y-200
160+200 = 40y-4y
360 = 36y
y = 10.

Applying the above obtained value of y in equation (i). We have,

x = [(4*10)+160]/5
x = (40+160)/5
x = 200 / 5
x = 40.

So you have \$40 whereas your friend has \$10.

(The reason why I supplemented Ms. Sue's answer is because I believed the question is asking for the initial amount of money both had, not after passing money along to the other.)

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