The sum of two numbers is 180 and the larger number exceeds four times the smaller number by ten, what are the 2 numbers?

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Answer 1 · 2015-10-02T21:02:30

The numbers are $110$ $110$ and $70$ $70$ .

Be $x$ $x$ and $y$ $y$ the two numbers. We know that

$x + y = 180$ $x+y=180$ and that

$x = y + 4 \cdot 10$ $x=y+4*10$

If we replace $x$ $x$ with $y + 40$ $y+40$ we find

$y + 40 + y = 2 y + 40 = 180$ $y+40+y=2y+40=180$

$\to 2 y = 180 - 40 = 140$ $rarr 2y=180-40=140$
$\to y = \frac{140}{2} = 70$ $rarr y=140/2=70$

Then we find

$x = 70 + 40 = 110$ $x=70+40=110$

$\to x + y = 110 + 70 = 180$ $rarr x+y=110+70=180$

Answer 2 · 2015-10-02T21:11:12

The numbers are: $34$ $34$ and $146$ $146$

The problem is to find such numbers, that:

These conditions lead to folowing system of equations:

${(x+y=180),(y=4x+10):}$

If we substitute $y$ in yje first equation we get:

$x+4x+10=180$
$5x+10=180$
$5x=170$
$x=34$

Now we can substitute $x$ in any equation to calculate $y$ :

$y=4*34+10$
$y=136+10$
$y=146$

Finally we can write the answer:

${(x=34),(y=136):}$