Question #c7539

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Question #c7539

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Answer 1 · 2017-10-12T11:50:32

See explanation

Explanation:

$10 = 40 %$ $10=40%$
$1 = 4 %$ $1=4%$
$1 \cdot 25 = 4 \cdot 25 %$ $1*25=4*25%$
$25 = 100 %$ $25=100%$

Answer 2 · 2017-10-12T16:30:29

Some explanation in detail

$40 % of 25 = 10$ $40%" of "25=10$

Explanation:

$Preamble$ $color(blue)("Preamble")$

The symbol % is a bit like a unit of measurement but one that is worth $\frac{1}{100}$ $1/100$

So, in the same way we would say $6 of x \to 6 x$ $6" of "x->6x$
We can say $40 of % \to 40 % = 40 \times \frac{1}{100} = \frac{40}{100}$ $40" of "%->40%=40xx1/100=40/100$

This compares very well to (picking some value at random) $3 c m$ $3cm$

centi $\to \frac{1}{100}$ $->1/100$

3 centimetres $\to 3 \times$ $-> 3xx$ centi of 1 metre $\to 3 \times \frac{1}{100} \times 1 metre$ $->3xx1/100xx1" metre"$

$= \frac{3}{100} metres$ $= 3/100" metres"$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Answering the question$ $color(blue)("Answering the question")$

$Breaking the question down into its component parts$ $color(brown)("Breaking the question down into its component parts")$

$40 %$ $40%$ of ........................... $\frac{40}{100} \times ?$ $40/100xx?$

Let the unknown value be represented by $x$ $x$ giving:
$40 %$ $40%$ of ........................... $\frac{40}{100} \times x \to \frac{40}{100} x$ $40/100xx x->40/100 x$

10 is .................................... $10 = ?$ $10=?$

10 is 40% of........................ $10 = \frac{40}{100} x$ $10=40/100x$

Multiply both sides by $\frac{100}{40}$ $color(red)(100/40)$
This changes the $\frac{40}{100}$ $40/100$ on the right into 1 so 'getting rid' if it, on that side.

$10 \times \frac{100}{40} d = d \frac{40}{100} \times \frac{100}{40} \times x$ $color(green)(10color(red)(xx100/40)color(white)("d")=color(white)("d")40/100color(red)(xx100/40)xx x)$

$\frac{100}{4} = x$ $100/4=x$

$x = 25$ $x=25$

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Question #c7539

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