Answer:
8 red
Step-by-step explanation:
r/2 = y - 2 = ⅓ × o = (w+3)/3
r + y + o + w = 35
r = 8, y = 6, o = 12, w = 9
Answer:
There are 8 red marbles
Step-by-step explanation:
Let the number of red be R , number of yellow be Y , number of orange be O and number of white be W. Then
[tex]R+Y+O+W=35[/tex] ..................... *
Half the number of red implies : [tex]\frac{R}{2}[/tex]
Two less than the number of yellow implies : [tex]y-2[/tex]
A third the number of orange implies : [tex]\frac{O}{2}[/tex]
A third of three more than the number of white marbles implies : [tex]\frac{1}{3}(W+3)[/tex]
combining everything together , we have
[tex]\frac{R}{2}=Y-2=\frac{O}{2}=\frac{1}{3}(W+3)[/tex]
[tex]\frac{R}{2}=Y-2[/tex] implies : [tex]R = 2(Y-2)=2Y-4[/tex] ................ equation 1
[tex]Y-2=\frac{O}{2}[/tex] implies : [tex]2(Y-2) = O[/tex]
therefore: [tex]O = 2Y-4[/tex] ...................... equation 2
[tex]Y-2 = \frac{1}{3}(W+3)[/tex] implies : [tex]3(Y-2)=W+3[/tex]
[tex]3Y-6=W+3[/tex]
Therefore: [tex]W=3Y-9[/tex] ......................... equation 3
Substituting equation 1 ,2 and 3 into equation * , we have
[tex]2Y-4+Y+3Y-6+3Y-9=35[/tex]
[tex]9Y-19=35[/tex]
[tex]9Y=35+19[/tex]
[tex]9Y=54[/tex]
[tex]Y=54/9[/tex]
[tex]Y=6[/tex]
substitute the values of Y , to get R , O and W
[tex]R=2Y-4[/tex]
[tex]R=2(6)-4[/tex]
[tex]R=12-4[/tex]
[tex]R=8[/tex]
[tex]O=3Y-6[/tex]
[tex]O=18-6[/tex]
[tex]O=12[/tex]
[tex]W=3Y-9[/tex]
[tex]W=18-9[/tex]
[tex]W=9[/tex]
Therefore:
number of red = 8
number of yellow = 6
number of orange = 12
number of white = 9
