White Jar
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If there are 36 bottuns in a jar and there are 3 times as many red bottuns as white bottuns, how many red?
If there are 36 buttons in a jar and there are 3 times as many red buttons as white buttons, how many red buttons are there?
You can go about this in several ways.....
Picture groups of 3 red buttons and 1 white button. The ratio is 3 to 1. Each group has 4 buttons. 36 buttons implies 9 groups of 4.
9 groups with 3 red buttons = 27 red buttons
9 groups with 1 red button = 9 red buttons.
27 is 3*9 and 27*9 = 36 CHECK
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Or
let r = the number of red buttons
let w = the number of white buttons
r + w = 36 (there are 36 buttons)
r = 3 * w (there are 3 times as many red buttons as white buttons)
Substitute 3w for r in the first equation
3w + w = 36
4w = 36 (combine like terms)
w = 9 (divide each side by 4)
So there are 9 white buttons.
since r = 3*w, there are 3*9 or 27 red buttons.
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Notice that the two methods give the same result...
27 red buttons
9 white buttons
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