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Novay_Z [31]
2 years ago
11

Ivan and Tanya share £150 in the ratio 4: 1 Work out how much more Ivan gets compared to Tanya.

Mathematics
1 answer:
Dennis_Churaev [7]2 years ago
7 0
Ivan gets £112.5(0) more than Tanya
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Rewrite tanx in terms of sinx and cosx
gulaghasi [49]

\tan x = \dfrac{\sin x}{\cos x}

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2 years ago
Nance is riding her bike to a friend’s house 4 and 1/2 miles away. She’s ridden 2 and 3/5 miles. How much farther does she need
Alinara [238K]
<h2>Hello!</h2>

The answer is:

She still needs to ride

1\frac{9}{10}miles

<h2>Why?</h2>

From the statement, we know that Nance's friend is 4 1/2 miles away and she only has ridden 2 3/5 miles.

So, let be "x" the distance that she still need to ride to get to her friend's house.

The equation will be:

TotalDistance=RiddenDistance+x

Remember that:

a\frac{b}{c}=a+\frac{b}{c}

Also, if we need to add/substract fractions we must remember that:

\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}

If we need to switch fractions to mixed numbers, we need to:

- Perform the division

- Keep the whole number and make a fraction with the aproximated next whole number (remainder) as numerator, and the original denominator. We need to use the remainder to approximate to the next whole number.

\frac{a}{b}=c.r

Where:

a=numerator\\b=denominator\\c=WholePart\\r=NextWholeNumber

So,

\frac{a}{b}=c\frac{r}{b}

Then, substituting the given information into the equation, we have:

4\frac{1}{2} =2\frac{3}{5} +x\\\\x=(4\frac{1}{2}) -(2\frac{3}{5})=4+\frac{1}{2}-2-\frac{3}{5}=2+\frac{1}{2}-\frac{3}{5}\\\\x=2+\frac{1}{2}-\frac{3}{5}=2+\frac{5-6}{10}=2-\frac{1}{10}\\\\x=2-\frac{1}{10}=\frac{20-1}{10}=\frac{19}{10}

So, she still need to ride \frac{19}{10}miles

or

1\frac{9}{10}miles

To prove if the answer is reasoable, let's substituite the obtained value into the equation and check if the equation is satisfied:

4\frac{1}{2}=2\frac{3}{5}+1\frac{9}{10}

4\frac{1}{2}=\frac{13}{5}+\frac{19}{10}

4\frac{1}{2}=\frac{9}{2}

4\frac{1}{2}=4\frac{1}{2}

Have a nice day!

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