Question 212507
Loretta's age now is twice John's age five years ago.
 In three years, the sum of John's and Loretta's ages will be 50. 
How old are Loretta and John today?
:
Let L = Loretta's present age
Let J = John's present age
:
"Loretta's age now is twice John's age five years ago."
L = 2(J - 5)
:
"In three years, the sum of John's and Loretta's ages will be 50":
(L+3) + (J+3) = 50
L + J + 6 = 50
L + J = 50 - 6
L + J = 44
:
Replace L with 2(J-5) in the above equation
2(J-5) + J = 44
2J - 10 + J = 44
2J + J = 44 + 10
3J = 54
J = {{{54/3}}}
J = 18 is John's present age
:
Find Loretta's age;
L = 2(18 - 5)
L = 2(13)
L = 26 yrs
;
Check this in the statement:
"In three years, the sum of John's and Loretta's ages will be 50":
18 + 3 + 26 + 3 = 
21 + 29 = 50
:
:
:
Fred is closing a bank account and wants to distribute the money among his grandchildren by giving each of them $20.00 
To do this, Fred, needs an additional $62.00. 
Instead, he gave each grandchild $17.00 and had $7.00 left over. 
How many grandchildren does Fred have? 
How much money did he have in the bank account?
:
Let n = no. of grandchildren
;
then from the given information, we can say:
(17n + 7) = amt he actually had in the bank
:
and what he wanted to do:
{{{(17n + 7 + 62)/n}}} = 20
{{{(17n + 69)/n}}} = 20
Multiply both side by n, results
17n + 69 = 20n
69 = 20n - 17n
69 = 3n
n = {{{69/3}}}
n = 23 grandchildren
and
17*23 + 7 = 
391 + 7 = $398, he actually had in the bank
:
:
Check solution using the $20 distribution:
{{{(398 + 62)/23}}} = 
{{{460/23}}} = $20; confirms our solutions