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2 years ago

Linda's penny bank is 1/4full. After she adds 360 pennies, it is 5/8 how many pennies can Linda bank hold?

Mathematics

2 answers:

Leokris [45]2 years ago

6 0

The answer for your question is 480.
Hope it helps!

ZanzabumX [31]2 years ago

5 0

X=# of pennies the bank can hold(1/2)x+80=(2/3)x80=(2/3)x-(1/2)x80=(4/6)x-(3/6)x80=(1/6)xx=80*6x=480 pennies (how many pennies the bank can hold)check: 1/2 full means 240 penniesadd 80 pennies240+80=320320/480=32/48=2/3

hope that helps

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<u>Solution-</u>

Given that,

In the parallelogram PQRS has PQ=RS=8 cm and diagonal QS= 10 cm.

Then considering ΔPQT and ΔSTF,

1- ∠FTS ≅ ∠PTQ ( ∵ These two are vertical angles)

2- ∠TFS ≅ ∠TPQ ( ∵ These two are alternate interior angles)

3- ∠TSF ≅ ∠TQP ( ∵ These two are also alternate interior angles)

<em>If the corresponding angles of two triangles are congruent, then they are said to be similar and the corresponding sides are in proportion.</em>

∴ ΔFTS ∼ ΔPTQ, so corresponding side lengths are in proportion.

$\Rightarrow \frac{PQ}{FS} =\frac{TQ}{TS} =\frac{TP}{TF}$

As QS = TQ + TS = 10 (given)

If TS is x, then TQ will be 10-x. Then putting these values in the equation

$\Rightarrow \frac{PQ}{FS} =\frac{TQ}{TS}$

$\Rightarrow \frac{8}{5} =\frac{10-x}{x}$

$\Rightarrow x=3.85$

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