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Answer:
3 Blue Umbrellas
Step-by-step explanation:
Given
[tex]B \to Blue[/tex]
[tex]Y \to Yellow[/tex]
[tex]R \to Red[/tex]
From the question, we have:
[tex]Y + R = 6[/tex] ---- i.e. 6 are not blue
[tex]B + R = 6[/tex] ---- i.e. 6 are not yellow
[tex]B + Y = 6[/tex] ---- i.e. 6 are not red
Required
The number of blue umbrellas
Make B the subject in: [tex]B + Y = 6[/tex]
[tex]B = 6 - Y[/tex]
Substitute: [tex]B = 6 - Y[/tex] in [tex]B + R = 6[/tex]
[tex]6 - Y + R = 6[/tex]
Collect like terms
[tex]R - Y = 6 - 6[/tex]
[tex]R - Y = 0[/tex]
Rewrite:
[tex]R = Y[/tex]
Substitute [tex]R = Y[/tex] in [tex]Y + R = 6[/tex]
[tex]Y + Y = 6[/tex]
[tex]2Y = 6[/tex]
Divide both sides by 2
[tex]Y=3[/tex]
Recall that: [tex]B = 6 - Y[/tex]
[tex]B = 6 - 3[/tex]
[tex]B = 3[/tex]