Question

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?

Answer 1

3 Blue Umbrellas

Explanation:

Given

`B \to Blue`

`Y \to Yellow`

`R \to Red`

From the question, we have:

`Y + R = 6` ---- i.e. 6 are not blue

`B + R = 6` ---- i.e. 6 are not yellow

`B + Y = 6` ---- i.e. 6 are not red

Required

The number of blue umbrellas

Make B the subject in:
`B + Y = 6`

`B = 6 - Y`

Substitute:
`B = 6 - Y` in
`B + R = 6`

`6 - Y + R = 6`

Collect like terms

`R - Y = 6 - 6`

`R - Y = 0`

Rewrite:

`R = Y`

Substitute
`R = Y` in
`Y + R = 6`

`Y + Y = 6`

`2Y = 6`

Divide both sides by 2

`Y=3`

Recall that:
`B = 6 - Y`

`B = 6 - 3`

`B = 3`