SOLUTION: 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?
Fred is closing a
Algebra.Com
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?
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?
Found 2 solutions by stanbon, ankor@dixie-net.com:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
---------
Now DATA:
Let John's age be "J" ; Let Loretta's age be "L"
------------------------------------
Equations:
L = 2(J-5)
(L+3)+(J+3)= 50
----
Substitute; then solve for J; then solve for L.
=======================================================
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 "a" be the amount of money in the bank account.
Let "g" be the number of grandchildren.
----------------------
Equations:
20g = x+62
---
17g = x-7
-----------------
Substitute for "x" and solve for "g":
20g = 17g+7+62
3g = 69
g = 23 (# of grandchildren)
------------------------------------
x = 17g+7
x = 17*23+7
x = $398 (amt in the bank)
===============================
Cheers,
Stan H.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 =
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:
= 20
= 20
Multiply both side by n, results
17n + 69 = 20n
69 = 20n - 17n
69 = 3n
n =
n = 23 grandchildren
and
17*23 + 7 =
391 + 7 = $398, he actually had in the bank
:
:
Check solution using the $20 distribution:
=
= $20; confirms our solutions
RELATED QUESTIONS
Loretta’s age in 17 years will be twice what it was 13 years ago. How old is Loretta... (answered by harpazo)
Loretta age in 19 years will be three times what it was 15 years ago. How old is Loretta... (answered by josmiceli)
The sum of Ellen’s and Todd’s ages is 34 years. Five years ago, the sum of twice... (answered by CubeyThePenguin,MathLover1)
In four years, John's age will be the same as Peter's age now. In two years, Peter's age... (answered by ikleyn,josgarithmetic)
John is twice as old as Peter. In 8 years, John’s age will be 2 more than the sum of... (answered by Edwin McCravy)
The sum of Leilah’s age and Abdul’s age is 34 years. Five years ago, the sum of... (answered by josgarithmetic)
John is five years younger than twice Becky’s age. Nine years ago, Becky was 16 years... (answered by josgarithmetic)
Loretta's age in 7 years will be three times what it was 9 years ago. How old is Loretta (answered by stanbon)
Loretta's age in 11 years will be three times what it was 7 years ago. How old is Loretta (answered by stanbon)