0
$\begingroup$

A $140$ feet long wire needs to be cut into two pieces such that one piece will be $\frac{2}{5}$ as long as the other. How many feet the shorter piece will be?

lets the shorter piece size be x

then the other piece size is 2x/5

now,

x + 2x/5 = 140

7x/5 = 140

x = 100

The answer is actually 40.

  • 2
    $2/5$ longer? Do you mean $2/5$ of a foot longer, or $2/5$ times the length of the other, or $1+2/5$ times the length of the other? Also, show what you've tried so far. It's poor form to submit a question without showing any sign of even trying. – 2017-02-24
  • 0
    This is a ratio question in disguise. – 2017-02-24
  • 0
    Updated my attempt the question wording correctly. – 2017-02-25
  • 0
    Out of $x$ and $2x/5$, which is smaller? – 2017-02-25

2 Answers 2

0

What you have done is correct. Only mistake is you have taken longer piece as x not shorter piece . Note that 2/5×X will be smaller than X. So the value 100 is of longer piece

So shorter piece's length will be 140-100=40

  • 0
    How can I do these things orally/mentally? I cannot imagine – 2017-02-25
  • 0
    What things which is shorter and which is longer? – 2017-02-25
  • 0
    Rather than algebra x,y how can I solve mentally – 2017-02-25
  • 0
    You have to follow same method. The calculation is quite easy to do it mentally. – 2017-02-25
2

Edit: This answer was suitable for the question asked originally. Now, the method is informative but the ratios have changed.

Let's call one bit $a$ and one bit $b$. $$ 140 = a + b $$

Let's relate the two. $b$ will be given by $$ b = \frac{7a}{5} $$

$$140 = a + \frac{7a}{5} $$

Make both expressions of a, have the same denominator $$140 = \frac{5a}{5} + \frac{7a}{5} $$

Add them $$140 = \frac{12a}{5} $$

Re-arrange $$a = \frac{700}{12} $$

$$b = \frac{7 \times 700}{5 \times 12} $$ $ a= 58.3333 $ recurring

$b = 81.6666666 $ recurring

  • 0
    Updated the wordings of the question - the answer is actually 40 – 2017-02-25