You can
put this solution on YOUR website!1.) One number is 3 more than the other. Their sum is 7. Find the numbers.
y=x+3, x+y=7 then x+x=3=7 then 2x=4 then x=2 and y=5
2.) The denominator of a fraction is twice the numerator. If the sum of the
terms is 3, what is the fraction?
fraction is x/2x x+2x=3x=3 then x=1 and fraction is 1/2
3.) The sum of two numbers is 165 and their difference is 29. Find the
numbers.
x+y=165
x-y=29
adding
2x=194
x=97 and y=68
4.) If the numerator of a certain fraction is increased by 6 and its
denominator is decreased by 5, the resulting fraction is equal to 3/4.
If the reciprocal of the original fraction is decreased by 1, the
resulting fraction is 16/9. Find the original fraction.
fraction is x/y
(x+6)/(y-5)=3/4
(y/x)-1=16/9
then
4(x+6)=3(y-5)
y/x=25/9
4x+24=3y-15
9y=25x
4x-3y=-39
-25x+9y=0
12x-9y=-117
-25x+9y=0
adding
-13x=-117
x=9
y=25
so fraction is 9/25
You can
put this solution on YOUR website!1.) One number is 3 more than the other. Their sum is 7. Find the numbers.
Let x = "one number
then
(x-3) = "other number
:
"Their sum is 7"
x + (x-3) = 7
2x = 7 + 3
x =
x = 5
:
Check: 5 - 3 = 2: 5 + 2 = 7
:
:
2.) The denominator of a fraction is twice the numerator. If the sum of the
terms is 3, what is the fraction?
Let x = the numerator
then
2x = denominator
Obviously, if x + 2x = 3, then x = 1 and the fraction is
:
:
3.) The sum of two numbers is 165 and their difference is 29. Find the
numbers.
x + y = 165
x - y = 29
------------adding eliminates y:
2x + 0 = 194
x =
x = 97
I'll let you find y
:
:
4.) If the numerator of a certain fraction is increased by 6 and its
denominator is decreased by 5, the resulting fraction is equal to 3/4.
=
:
If the reciprocal of the original fraction is decreased by 1, the
resulting fraction is 16/9.
- 1 =
=
+ 1
=
+
=
Find the original fraction.
:
;
Check solution in the 1st statement:
=
=
=
; confirms our solutions
:
