- Juwan and Jake both have money in their pockets. If Juwan gave Jake 15 cent then they both would have the same amount of money. However, if Jake gave Juwan 15 cent , then Juwan would have 5 times as much money as Jake would have. How much money do Juwan and Jake have together?

- There are three girls in the Hassen family. Donna's age plus Eve's age is 33 years. Donna's ages plus Fran's age is 31 years. Eve's age plus Fran's age is 26 tears . Write the age of each of the three girls.?

if Juwan=w and Jake=k,

w-15 = k+15
w+15 = 5(k-15)
so,
w=60
k=30

So, Juwan has 60 cents, Jake has 30 cents
60-15 = 30+15
60+15 = 5(30-15)
------------------------------
d+e = 33
d+f = 31
e+f = 26

e = 33-d, so
d+f = 31
33-d+f = 26
2f = -6
eh? is there a typo?

Let's solve these two problems step by step:

1. Juwan and Jake's Money:
Let's assume Juwan has x cents and Jake has y cents.
According to the given information, if Juwan gave Jake 15 cents, they would both have the same amount of money.
So, Juwan would then have (x-15) cents and Jake would have (y+15) cents.

Also, if Jake gave Juwan 15 cents, Juwan would then have 5 times as much money as Jake.
So, Juwan would have (x+15) cents and Jake would have (y-15) cents.

From the above information, we can write two equations:
1. (x-15) = (y+15)
2. (x+15) = 5(y-15)

We can solve these equations to find the values of x and y.

Solving equation 1:
x - 15 = y + 15
x - y = 30 (Equation 3)

Solving equation 2:
x + 15 = 5(y - 15)
x + 15 = 5y - 75
x - 5y = -90 (Equation 4)

Now we have two equations (Equation 3 and Equation 4) to solve simultaneously.

Multiplying Equation 3 by 5 and adding it to Equation 4:
5(x - y) + (x - 5y) = 5(30) - 90
5x - 5y + x - 5y = 150 - 90
6x - 10y = 60 (Equation 5)

Simplifying Equation 5:
6x - 10y = 60
12x - 20y = 120 (Multiplying both sides by 2)

Subtracting Equation 5 from Equation 4:
12x - 20y - 6x + 10y = 120 - 60
6x - 10y = 60

We can see that Equation 4 is the same as Equation 5, so we have infinitely many solutions. This means we cannot determine the exact values of x and y, and therefore cannot determine how much money Juwan and Jake have together.

2. Ages of the Three Girls:
Let's assume Donna's age is x, Eve's age is y, and Fran's age is z.

According to the given information:
1. x + y = 33 (Equation 6)
2. x + z = 31 (Equation 7)
3. y + z = 26 (Equation 8)

We have three equations (Equation 6, Equation 7, and Equation 8) to solve simultaneously to find the ages of the three girls.

Adding Equation 6, Equation 7, and Equation 8:
(x + y) + (x + z) + (y + z) = 33 + 31 + 26
2x + 2y + 2z = 90

Dividing by 2:
x + y + z = 45 (Equation 9)

Subtracting Equation 6 from Equation 9:
(x + y + z) - (x + y) = 45 - 33
z = 12

Substituting the value of z in Equation 7:
x + 12 = 31
x = 19

Substituting the values of x and z in Equation 6:
19 + y = 33
y = 14

Therefore, the ages of the three girls are:
Donna's age (x) = 19 years
Eve's age (y) = 14 years
Fran's age (z) = 12 years

To solve the first problem, let's assume that Juwan has x cents and Jake has y cents.

According to the problem, if Juwan gives 15 cents to Jake, they would have the same amount of money. So, Juwan would have (x - 15) cents and Jake would have (y + 15) cents.

It is also stated that if Jake gives 15 cents to Juwan, then Juwan would have 5 times as much money as Jake would have. So, Juwan would have (x + 15) cents and Jake would have (y - 15) cents.

Now we have two equations:

1) (x - 15) = (y + 15)
2) (x + 15) = 5(y - 15)

We can solve these two equations simultaneously to find the values of x and y.

From equation 1, we can rearrange it as: x - y = 30. (Equation 3)

Now, let's substitute x + 15 in the second equation with (y + 15) according to equation 1:

(y + 15 + 15) = 5(y - 15)
y + 30 = 5y - 75
4y = 105
y = 26.25

Now, substitute the value of y into equation 3:

x - 26.25 = 30
x = 56.25

So, Juwan has 56.25 cents and Jake has 26.25 cents.

To find the total money Juwan and Jake have together, we add their amounts:

56.25 cents + 26.25 cents = 82.50 cents

Therefore, Juwan and Jake have a total of 82.50 cents together.

Moving on to the second problem:

Let's assume Donna's age is x, Eve's age is y, and Fran's age is z.

According to the problem, we have three equations:

1) x + y = 33
2) x + z = 31
3) y + z = 26

We can solve these three equations simultaneously to find the values of x, y, and z.

From equation 1, we can rewrite it as: x = 33 - y. (Equation 4)

Let's substitute x in equation 2 with (33 - y) according to equation 4:

33 - y + z = 31
z = y - 2. (Equation 5)

Now, substitute x in equation 3 with (33 - y) according to equation 4:

y + z = 26
y + (y - 2) = 26
2y - 2 = 26
2y = 28
y = 14

Using equation 4: x = 33 - 14 = 19
Using equation 5: z = 14 - 2 = 12

Therefore, Donna's age is 19, Eve's age is 14, and Fran's age is 12.