Posted by Anonymous on .
one number is three more than a second number. Three times the first is 7 less than 2 times the second. Find the numbers.
The value of the second number is ___

math 
Reiny,
second number  x
first number  x+3
A lot of students have difficulty translating an English inequality statement like "Three times the first is 7 less than 2 times the second" into an equation.
Here is the way I used to teach this: ..
Reword the statement as
"Three times the first is less than 2 times the second by 7"
now translate that
3(x+3) < 2(x) by 7
let's add that difference of 7 to the smaller side, now they would be equal
3(x+3) + 7 = 2(x)
3x + 9 + 7 = 2x
x = 16
so second number is 16, he first is 13
check:
3 times the first = 3(13) = 39
2 times the second = 2(16) = 32
is 39 7 less than 32 ??? YEAHH!