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.
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:
The tens digit of a certain number is 4 more than the unit digit.
Replace the words "The tens digit of a certain number" by t. and you have
t is 4 more than the unit digit.
replace the words "the units digit" by u
t is 4 more than u.
Replace the words "4 more than u" by "u + 4".
t is u+4
Replace the word "is" by an equal sign "=".
t = u+4
That's the first equation. Let's get the second one:
it is seven times as large as the sum of its digits.
Replace the word "it" by 10t+u
10t+u is seven times as large as the sum of its digits.
Replace the words "the sum of its digits" by "(t+u)"
10t+u is seven times as large as (t+u).
Replace the words "seven times as large as" by "7" in front of the parentheses.
10t+u is 7(t+u)
Replace the word "is" by an equal sign "=".
10t+u = 7(t+u)
That's your second equation.
So you have this system:
ìt = u+4
í
î10t+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
