# math

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1)
Larry is 8 yrs older than his sister.In 3 yrs, hr will be twice as old as she will be then.how old is each now?

2)
Jennifer is 6 yrs older than Sue. in 4 yrs, she will be twice as old as Sue was 5 yrs ago. Find their ages now.

3)
Adam is 5 yrs younger than Eve. In 1 yr, Eve will be three times as old as Adam was 4 yrs ago. Find their ages now.

4)jack is twice as old as Jill. In 2 yrs, Jack will be 4 times as old as Jill was ( uears ago. How old are they now?

5)
four yrs ago, Katie was twice as old as Anne was then. In 6 yrs, Anne will be the same age that Katie is now How old is each now?

6)
five yrs ago, Tom was one third as old as his father was then. In 5 yrs Tom will be half as old as his father will be then. Find their ages now.

7)
Barry is 8 yrs older than sue. In 4 yrs, she will be twice as old as Sue was 5 yrs ago. find their ages now.

• math -

1. Larry's sister = X yrs old.
Larry = (X+8)yrs old.

In 3 yrs:
Larry = X+11.
Sister = X+3.

X+11 = 2(X+3),
X+11 = 2X+6,
X-2X = 6-11,
-X = -5,
X = 5yrs = sister's age.
X+8 = 5+8 = 13YRS = Larry's age.

2. Sue = X yrs old.
Jennifer = (x+6) yrs old.

X+10 = 2(X-5),
X+10 = 2X-10,
X-2X = -10-10,
-X = -20,
X = 20 yrs = Sue's age.
x+6 = 20+6 = 26 yrs = Jennifer's age.

3. Eve = X yrs old.

X+1 = 3(X-5-4). Solve for X.

4. Jill = X yrs old.
Jack = 2x yrs old.

4(x-7) = 2x+2. Solve for x.

5. 4 yrs ago: Anne = x yrs old; Katie = 2x yrs old.

NOW: Anne=(x+4)yrs old; Katie = (2x+4)
yrs old.

x+10 = 2x+4.
x-2x = 4-10,
-x = -6,
x = 6.

x+4 = 6+4 = 10yrs = Anne's age.
2x+4 = 2*6 + 4 = 16 yrs = Katie's age.

6. 5yrs ago: Tom's father = x yrs old.
Tom = x/3 yrs old.

NOW: Tom's father = (x+5)yrs old.
Tom = (x/3+5)yrs old.

5yrs from now:
(x/3+10) = (x+10)/2 = (x/2)+5,
(x/3)+10 = (x/2)+5,
x/3-x/2 = 5-10 = -5,
Multiply both sides by 6:
2x-3x = -30,
-x = -30,
x = 30.

x+5=30+5 = 35 yrs = Tom's father's age.

x/3+5 = 30/3 + 5 = 15yrs = Tom's age.

7. NOW: Sue = x yrs old.
Barry = (x+8)yrs old.

4 yrs from now:
x+12 = 2(x-5). Solve for x and (x+8).

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