Question 489605
 can you pls answer this word problem: 
The tens digit of a certain number is 4 more than the unit digit. Find the integer if it is seven times as large as the sum of its digit. 
<pre>
The suffix "-ty" means "times ten".  Illustrations:

six-ty means six times ten
seven-ty means seven times ten
eight-ty means eight times ten
nine-ty means "nine times ten.

The word that comes after "six-ty", as in sixty three, means 
that three is added to six times ten.

So six-ty-three means "ten times six plus three", or 10×6+3 or 63.

That's why a number is ten times the tens digit plus the units digit.

So the number is 10t+u where t is the tens (or first) digit and u is
the ones or units (or second) digit.

Take the first sentence above:
</pre>
The tens digit of a certain number is 4 more than the unit digit. 
<pre>
Replace the words "The tens digit of a certain number" by t. and you have
</pre>
t is 4 more than the unit digit.
<pre>
replace the words "the units digit" by u
</pre>
t is 4 more than u.
<pre>
Replace the words "4 more than u" by "u + 4".
</pre>
t is u+4
<pre>
Replace the word "is" by an equal sign "=".
</pre>
t = u+4
<pre>
That's the first equation.  Let's get the second one:
</pre>
it is seven times as large as the sum of its digits.
<pre>
Replace the word "it" by 10t+u
</pre>
10t+u is seven times as large as the sum of its digits.
<pre>
Replace the words "the sum of its digits" by "(t+u)"
</pre>
10t+u is seven times as large as (t+u).
<pre>
Replace the words "seven times as large as" by "7" in front of the parentheses.
</pre>
10t+u is 7(t+u)
<pre>
Replace the word "is" by an equal sign "=".
</pre>
10t+u = 7(t+u)
<pre>
That's your second equation.

So you have this system:

<font face = "symbol">ì</font>t = u+4
<font face = "symbol">í</font>
<font face = "symbol">î</font>10t+u = 7(t+u)

Can you solve that system? If you can't post again asking how.

Answer t=8, u=4  Then number is therefore 84.

Checking in the words, not the equations:

The tens digit, 8, of a certain number, 84 is 4 more than the unit digit, 4.

It's certainly true that 8 is 4 more than 4

"it, 84, is seven times as large as the sum of its digit, 8+4 or 12.

84 is certainly 7 times as large as 12.

Edwin</pre>