Question 161160: 1.one number is 11 more than another number. find the two numbers if three times the larger number exceeds four times the smaller number by 4.
2.if the first of two consecutive integers is multiplied by 3, this product is 20 more than the sum of the two integers. find the integers.
3.five times the first of three consecutive even integers is 4 less than twice the sum of the second and third. find the integers.
4.the sum of three numbers is 49. the second number is three times the first number and the third number is 6 less than the first number. find the three numbers.
5.the numerator of a fraction is 2 more than the numerator. if the numerator is decreased by one and the denominator is increased by 2, the value of the original fraction and the new one is 7/3. find the original fraction.
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! 1.
one number  is 11 more than another number  .
..(1)
find the two numbers, and , if three times the larger number(  ) exceeds four times the smaller number () by  .
..(2)
Now solve the system:
..(1)
.plug } value in ( )
..(2)
------------------------------------------------
..(2)
find
plug value in ( ) to find
..(1)
2. If the first of two consecutive integers is multiplied by 3, this product is 20 more than the sum of the two integers. Find the integers.
remember:  ,  , and  are three consecutive integers
. first of two consecutive integers
. second of two consecutive integers
.
.
.
. first of two consecutive integers
. second of two consecutive integers
Check:
.
.
.
.
3. Five times the first of three consecutive even integers is 4 less than twice the sum of the second and third. Find the integers.
remember: , , and  are three consecutive even integers
. first of three consecutive integers
. second of three consecutive integers
.third of three consecutive integers
.
.
.
.
. first of three consecutive integers
. second of three consecutive integers
.third of three consecutive integers
Check:
.
.
.
.
.
4. The sum of three numbers is 49. The second number is three times the first number and the third number is 6 less than the first number. Find the three numbers.
. first of three numbers
. second of three numbers
. third of three numbers
Check:
5. The numerator of a fraction is 2 more than the denominator. If the numerator is decreased by one and the denominator is increased by 2, the value of the original fraction and the new one is 7/3. Find the original fraction.
let a fraction be 
if the numerator  of a fraction is  , we have
If the numerator is decreased by and the denominator  is increased by , the value of the original fraction and the new one is  , or
plug in and find
so, the original fraction is:
 .....where
 and 
check:
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