I have 3 math problems i can't get. can anyone help me? and don't say and rude comments! ?

Question

the first one says the sum of two numbers is 27. One half of the first number plus one third of the second number is 11. Find the numbers using a system of equations.

the second one says roberta is 25 years older than her daughter cindy. in four years roberta will be twice as old as cindy. how old are they now?

the last one is a collection of dimes and quaters is worth $3.55. There are 25 coins in all. How many quarters are there?

use the system of equations. not guess and check. thank you! all help is appreciated.

Answer 1

1) "the sum of two numbers is 27" means there exist numbers a and b such that a + b = 27.

"One half of the first number plus one third of the second number is 11" translates into (1/2)a + (1/3)b = 11.

Thus we obtain the following system of linear equations:

a + b = 27.

(1/2)a + (1/3)b = 11

We now use substitution to solve for one of the variables.

From the 1st equation we have a = 27 - b

Substitute into the second (1/2)(27-b) + (1/3)b = 11

(27/2)-(1/2)b+(1/3)b = 11

-(1/2)b+(1/3)b = -(5/2)

-(1/6)b = -(5/2)

b = (30/2) = 15

Now that we have solved for b.  Plug this back into the 1st equation.

a + 15 = 27

a = 27-15 = 12

Thus a = 12 and b = 15

2) Take R to be the age of roberta and C to be the age of cindy.

"roberta is 25 years older than her daughter cindy" Thus:

R = C + 25

"in four years roberta will be twice as old as cindy" Thus:

R+4 = 2(C+4)

R+4 = 2*C + 8

R = 2*C + 4

Thus we have two equations:

R = C + 25

R = 2*C + 4

C + 25 = 2C + 4

25 = C + 4

21 = C

Thus Cindy is 21 and by the first equation Roberta is 46.

3) D is the number of dimes. Q is the number of quarters.

"a collection of dimes and quarters is worth $3.55" means:

.10*D + .25*Q = 3.55

"here are 25 coins in all"

D + Q = 25

Thus we must solve the system:

D + Q = 25

.10*D + .25*Q = 3.55

Use the same method used in question 1.