# algebra

At a banquet the ratio if the number of boys to the number of girls is 5:3. Halfway tjrough the banquet 20 boys leave and the ratio bexomes 5:4. How many girls are at thebbanquet?

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1. let the number of boys be 5x
let the number of girls be 3x

during banket, 20 boys leave
(5x-20)/3x = 5/4
20x - 80 = 15x
5x = 80
x = 16

number of girls is 3x or 48.

check:
original:
boys = 80
girls = 48

after leaving:
boys = 60
girls = 48
ratio is 60:48 = 5 : 4

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2. reiny can you explain the equation more? is the / a division symbol? i still don't understand how you got 16.

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3. 48

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4. ratios are fractions so yes the "/" is a division sign. the 2 ratios become 5/3=5/4, but you have to incorporate the minus 20. So 5x-20 represent to boys, and 3x is the girls then to make it equate the 5:4 ratio you place it in an algebraic equation and cross multiply. (5x-20) X 4= 3x X 5 = 20x-80= 15x
20x-15x= 80 = 5x=80 or x =80/5 which equals 16,so x =16.

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5. Where you get the 80 from...?

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