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Theresa has an umbrella stand at the beach. - All of them are blue, except for six. - All of them are yellow, except for six. - All of them are red, except for six. How many blue umbrellas does Theresa have?

Sagot :

MrRoyal

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]

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