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Serggg [28]
2 years ago
11

Tim and three friends go on holiday together for a week. The 4 friends will share the costs of the holiday equally. Here are the

costs of the holiday. Work out how much Tim has to pay for his share of the costs.
Mathematics
1 answer:
castortr0y [4]2 years ago
5 0

Answer: £535

Step-by-step explanation:

Herr is the complete question:

Tim and three friends go on holiday together for a week.

The 4 friends will share the costs of the holiday equally,

Here are the costs of the holiday.

£1280 for 4 return plane tickets

£640 for the villa

£220 for hire of a car for the week

Work out how much Tim has to pay for his share of the costs.

Firstly, we have to calculate the total cost of the holiday. This will be:

= £1280 + £640 + £220

= £2140

We are also told that they will share the costs equally. Since there are 4 people, Tim will have to pay:

= £2140 ÷ 4

= £535

Tim will pay £535

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Step-by-step explanation:

Refer to attachment for marking of sides.

In the given figure , ∆ABC , ∆ABD and ∆ADC are right angled triangles . Therefore here we can use the Pythagoras theorem , as ,

\longrightarrow base² + perpendicular² = hypotenuse ² .

<u>•</u><u> </u><u>In </u><u>∆</u><u>A</u><u>B</u><u>D</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>;</u>

\longrightarrow AB² + BD² = AD²

\longrightarrow AB² + x² = 10²

\longrightarrow AB² = 10² - x²

\longrightarrow AB² = 100 - x²

\rule{200}2

<u>•</u><u> </u><u>Again</u><u> </u><u>in </u><u>∆</u><u>A</u><u>D</u><u>C</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>;</u>

\longrightarrow AC² + AD² = CD²

\longrightarrow AC² = 20² - 10²

\longrightarrow AC² = 400 - 100

\longrightarrow AC² = 300

\rule{200}2

<u>Again</u><u> </u><u>in </u><u>∆</u><u>A</u><u>B</u><u>C</u><u> </u><u>,</u><u> </u><u>we </u><u>have</u><u> </u><u>,</u>

\longrightarrow AC² = AB² + BC²

Substituting the values from above ,

\longrightarrow 300 = 100-x² + (20-x)²

\longrightarrow 300 = 100 - x² + 400 + x² - 40x

\longrightarrow 40x = 500 - 300

\longrightarrow 40x = 200

\longrightarrow x = 200/40

\longrightarrow x = 5

<h3>Hence the required answer is 5 .</h3>

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