SOLUTION: Hi 3/8 of the buttons are green. There were 20 more blue buttons than green. The remaining 84 buttons were pink. How many buttons were blue

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Question 1206221: Hi
3/8 of the buttons are green. There were 20 more blue buttons than green. The remaining 84 buttons were pink. How many buttons were blue
Found 4 solutions by Theo, ikleyn, josgarithmetic, math_tutor2020:
Answer by Theo(13342) About Me  (Show Source):
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T = total
G = green
B = blue
P = pink

T = G + B + P
P = 84 so .....
T = G + B + 84
3/8 of the buttons are green, so .....
T = 3/8 * T + B + 84
there are 20 more blue buttons than green, so .....
T = 3/8 * T + 3/8 * T + 20 + 84
combine like terms to get:
T = 6/8 * T + 104
subtract 6/8 * T from both sides of the equation to get:
2/8 * T = 104
solve for T to get:
T = 104 * 8/2 = 416

since T = 416 and P = 84, then .....
416 = G + B + 84
subtract 84 from both sides of the equation to get:
332 = G + B
since G = 3/8 * T, then .....
G = 3/8 * 416 = 156
since B = G + 20, then .....
B = 176

you have:

T = 416
P = 84
G = 156
B = 176

since T = G + B + P, then .....
T = 156 + 176 + 84 = 416.

your solution is that there were 176 blue buttons.

Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.
3/8 of the buttons are green. There were 20 more blue buttons than green.
The remaining 84 buttons were pink. How many buttons were blue
~~~~~~~~~~~~~~~~~~~~


        It can be easily solved using only ONE unknown and one equation.
        See my solution below. 


Let x be the total number of buttons.

Then  %283%2F8%29x  buttons are green;  %283%2F8%29x%2B20  buttons are blue 
and remaining 84 buttons are pink.  


So, we can write this equation for total

    %283%2F8%29x + %283%2F8%29x%2B20 + 84 = x.


At this point, the setup is complete.
To solve equation, multiply both sides by 8

    3x + 3x + 160 + 672 = 8x

    160 + 672 = 8x - 3x - 3x 

       832    =      2x

       x      =    832/2 = 416.


The number of blue buttons was  %283%2F8%29%2A416 + 20 = 176.    ANSWER

Solved, using only one unknown.



Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!

BUTTON COLOR    HOW MANY

GREEN            3T/8

BLUE             3T/8+20 

PINK             84

TOTAL             T

In that way, question asks for 3T%2F8%2B20.

3T%2F8%2B%283T%2F8%2B20%29%2B84=T
-
6T%2F8%2B20%2B84=T
3T%2F4%2B104=T
104=T%2F4
highlight_green%28T=416%29

The answer for the question
%283%2F8%29416%2B20
highlight%28176%29------number of blue buttons

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: 176

Work Shown
b = number of blue buttons
b-20 = number of green buttons
84 = number of pink buttons
blue+green+pink = b+(b-20)+84 = 2b+64 = total number of buttons

3/8 of total = number of green
(3/8)*(2b+64) = b-20
3(2b+64) = 8(b-20)
6b+192 = 8b-160
192+160 = 8b-6b
352 = 2b
b = 352/2
b = 176